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theory, the stable module category is a quotient of a module category in which projectives are "factored out." Let R be a ring. For two modules M and N over
Stable_module_category
Category whose objects are R-modules and whose morphisms are module homomorphisms
{\displaystyle R} , the category of left modules over R {\displaystyle R} is the category whose objects are all left modules over R {\displaystyle R}
Category_of_modules
Category in mathematics
triangles". Prominent examples are the derived category of an abelian category, as well as the stable homotopy category. The exact triangles generalize the short
Triangulated_category
In category theory, a branch of mathematics, a stable ∞-category is an ∞-category such that (i) It has a zero object. (ii) Every morphism in it admits
Stable_∞-category
R-modules. On the other hand, the category of pointed topological spaces and the category of pointed simplicial sets are not stable model categories. Any
Stable_model_category
Mathematical object
right) module spectra is stable; hence, it can be considered as either analog or generalization of the derived category of modules over a ring. Lurie defines
Module_spectrum
Algebraic structure
In mathematics, given a group G {\displaystyle G} , a G-module is an abelian group M {\displaystyle M} on which G {\displaystyle G} acts compatibly with
G-module
sets, any set with at least two elements is a cogenerator. In the category of modules over a ring R, a generator in a finite direct sum with itself contains
Generator_(category_theory)
In mathematics, a module that has a basis
mathematics, a free module is a module that has a basis, that is, a generating set that is linearly independent. Every vector space is a free module, but, if the
Free_module
Category with direct sums and certain types of kernels and cokernels
prototypical example of an abelian category is the category of abelian groups, Ab. Abelian categories are very stable categories; for example they are regular
Abelian_category
Generalization of vector bundles
abelian category, a full subcategory of the category of O X {\displaystyle {\mathcal {O}}_{X}} -modules. (Analogously, the category of coherent modules over
Coherent_sheaf
Mathematical object
different categories of spectra leading to many technical difficulties, but they all determine the same homotopy category, known as the stable homotopy
Spectrum_(topology)
NASA crewed Moon landing spacecraft (1969–1972)
The Apollo Lunar Module (LM /ˈlɛm/), originally designated the Lunar Excursion Module (LEM), was the lunar lander spacecraft that was flown between lunar
Apollo_Lunar_Module
Concept in homological algebra
of triangulated categories or functors between them, for example stable homotopy category can be shown not to arise from a dg category in this way. However
Differential_graded_category
Mathematical concept
compact objects in the category of sets are precisely the finite sets. For a ring R, the compact objects in the category of R-modules are precisely the finitely
Compact_object_(mathematics)
Assembly of photovoltaic cells used to generate electricity
device that converts sunlight into electricity by using multiple solar modules that consists of photovoltaic (PV) cells. PV cells are made of materials
Solar_panel
Example of the Koszul duality
derived category of coherent sheaves on the projective space P ( V ) {\displaystyle \mathbb {P} (V)} and the stable category of graded modules gr ∧ V {\displaystyle
BGG_correspondence
Branch of mathematics that studies algebraic structures
quotient module etc. Tensor product Advanced concepts: Category theory Category of groups Category of abelian groups Category of rings Category of modules (over
List of abstract algebra topics
List_of_abstract_algebra_topics
Generalization of a category
specifically category theory, a quasi-category (also called quasicategory, weak Kan complex, inner Kan complex, infinity category, ∞-category, Boardman complex
Quasi-category
being projective. It is useful in defining the Heller operator in the stable category, and in giving elementary descriptions of dimension shifting. Schanuel's
Schanuel's_lemma
single-parameter persistence module M {\displaystyle M} is a functor M : T → V e c K {\displaystyle M:T\to \mathbf {Vec} _{K}} from the poset category of T {\displaystyle
Persistence_module
Type of computer memory
signal. Registered memory allows a computer system to remain stable with more memory modules than it would have otherwise. When conventional memory is compared
Registered_memory
Mathematical category with weak equivalences, fibrations and cofibrations
a model category structure, such as the category of simplicial sets. Another model category is the category of chain complexes of R-modules for a commutative
Model_category
Concept in homological algebra
{D}}^{\leq 0},{\mathcal {D}}^{\geq 0})} of a triangulated category or stable infinity category which abstract the idea of complexes whose cohomology vanishes
T-structure
Various mathematical dualites
stable category of finite-dimensional graded modules over an exterior algebra to the bounded derived category of coherent sheaves on projective space. The
Koszul_duality
General-purpose programming language
to a top-level declaration: Example: // Class is visible only to current module internal open class TalkativeButton { // method is only visible to current
Kotlin
Most general completion of a commutative square given two morphisms with same codomain
that all pullbacks exist in the category of groups and in the category of modules over some fixed ring. In the category of sets, the pullback of functions
Pullback_(category_theory)
Homomorphisms between simple modules over the same ring are isomorphisms or zero
R} -modules. The group version is a special case of the module version, since any representation of a group G can equivalently be viewed as a module over
Schur's_lemma
Modular space station in low Earth orbit
plans for the ISS include the addition of at least one module, the Payload Power Thermal Module by Axiom Space, forming the commercial segment of the station
International_Space_Station
Guidance and navigation computer used in Apollo spacecraft
program that was installed on board each Apollo command module (CM) and Apollo Lunar Module (LM). The AGC provided computation and electronic interfaces
Apollo_Guidance_Computer
canonical divisor) category The category of modules over a ring is the category where the objects are all the (say) left modules over the given ring
Glossary_of_module_theory
Second crewed Moon landing
Conrad and Lunar Module Pilot Alan L. Bean completed just over one day and seven hours of lunar surface activity while Command Module Pilot Richard F.
Apollo_12
Maps whose domain and codomain are acted on by the same group, and the map commutes
Groups, Rings, Modules, Dover Books on Mathematics, Dover Publications, pp. 86–87, ISBN 9780486490823. Segal, G. B. (1971), "Equivariant stable homotopy theory"
Equivariant_map
Analysis of datasets using techniques from topology
distance is the terminal object in a poset category of stable metrics on multidimensional persistence modules in a prime field. Sheaves, a central concept
Topological_data_analysis
Category
common examples: The category of (left) modules over a ring R, in particular: the category of vector spaces over a field K. The category of (Hausdorff) abelian
Pre-abelian_category
Cohomology theory
_{K(n)_{*}}K(n)_{*}(Y).} They are "fields" in the category of ring spectra. In other words every module spectrum over K(n) is free, i.e. a wedge of suspensions
Morava_K-theory
Concept in math
category, let A be a Grothendieck abelian category, for example the category of modules over a ring or the category of sheaves of abelian groups on a topological
Homotopy_category
Third crewed mission of the Apollo space program
three-man crew consisted of Commander James McDivitt, Command Module Pilot David Scott, and Lunar Module Pilot Rusty Schweickart. Flown in low Earth orbit, it
Apollo_9
Concerned with the notion of stability in model theory
\kappa } -stable for all infinite κ {\displaystyle \kappa } . Some further examples of stable theories are listed below. The theory of any module over a
Stable_theory
Concept in mathematics regarding sets operating on groups
Given any group G, (G, ∅) is trivially a group with operators Given a module M over a ring R, R acts by scalar multiplication on the underlying abelian
Group_with_operators
Object detection system
network is removed, and for every possible object class, initialize a network module at the last layer ("regression network"). The base network has its parameters
You_Only_Look_Once
Linux kernel security module
Security-Enhanced Linux (SELinux) is a Linux kernel security module that provides a mechanism for supporting access control security policies, including
SELinux
Lightweight programming language
values at run time), coroutines (cooperative multitasking) and dynamic module loading. The classic "Hello, World!" program can be written as follows,
Lua
Type of cryptocurrency that is reserve backed
A stablecoin is a type of cryptocurrency that aims to maintain a stable value relative to a specified asset, a pool or basket of assets. The specified
Stablecoin
Construction in algebra
The axioms are partly chosen so that the category of H-modules is a rigid monoidal category. The unit H-module is the separable algebra HL mentioned above
Hopf_algebra
Software platform
divided in the following categories: Aggregates, Color, Date and Time, Logic, Math, String, Type Cast, and Advanced. An Ignition Module SDK is available for
Ignition_SCADA
Free and open-source 3D CAD software
to add building information modeling (BIM) functionality with the Arch Module. FreeCAD has a modular structure built from a set of workbenches, where
FreeCAD
Monoidal category
ISBN 978-3-540-38955-2 Iwanari, Isamu (2018), "Tannaka duality and stable infinity-categories", Journal of Topology, 11 (2): 469-526, arXiv:1409.3321, doi:10
Tannakian_formalism
Chinese modular space station (since 2021)
core module, Tianhe, was launched in April 2021 and was followed by the Wentian and Mengtian experiment modules in July and October 2022; The modules were
Tiangong_space_station
Programming language derived from Perl
requests that modules be identified by name, version, and authority. It is possible to load only a specific version of a module, or even two modules of the same
Raku_(programming_language)
Hypothesis in mathematical category theory
Eilenberg–MacLane space, crossed module. Algebraic homotopy N-group (category theory) Pursuing Stacks Quasi-category Stratified space Kapranov, M. M.;
Homotopy_hypothesis
Game programming library
particle system module for raylib spine-raylib – Spine animations integration module for raylib cimgui-raylib – Dear Imgui integration module for raylib In
Raylib
Multi-stage paper folding technique
unit origami is a multi-stage paper folding technique in which individual modules or units are created out of sheets of paper and assembled into a flat shape
Modular_origami
Cohomology class
S-modules (see Elmendorf et al., 2007). S-modules possess a model structure, whose homotopy category is the stable homotopy category. In S-modules the
Highly structured ring spectrum
Highly_structured_ring_spectrum
Type of nuclear fission reactor
deliver an electrical power output as low as 10 MWe and up to 300 MWe per module. Reactors below 10 MWe in capacity are considered nuclear microreactors
Small_modular_reactor
Mathematical ring with well-behaved ideals
Lemma 25.4. Anderson, Frank W.; Fuller, Kent R. (1992), Rings and categories of modules, Graduate Texts in Mathematics, vol. 13 (2 ed.), New York: Springer-Verlag
Noetherian_ring
Spectral sequence
makes H*(X) a module over the algebra of its stable cohomology operations, the Steenrod algebra A. Thinking about H*(X) as an A-module forgets some cup
Adams_spectral_sequence
Theory in mathematics
universal among the split-exact, homotopy invariant and stable additive functors on the category of the separable C*-algebras. Any such theory satisfies
KK-theory
Generalization of algebraic variety
category of OX-modules, which are sheaves of abelian groups on X that form a module over the sheaf of regular functions OX. In particular, a module M
Scheme_(mathematics)
Method to produce electricity from solar radiation
electricity generation and as photosensors. A photovoltaic system employs solar modules, each comprising a number of solar cells, which generate electrical power
Photovoltaics
Company based in Riga, Latvia
LTE Category 7, Band 28/32 , and full carrier aggregation card. First stable RouterOS release featuring device-mode and allowed-versions. First stable VXLAN
MikroTik
a simple module is precisely a simple object in the category of (say left) modules. simplex category The simplex category Δ is the category where an object
Glossary_of_category_theory
Theory in neuropsychology
neuron in it to represent a category to which input vectors are classified. After the input vector is classified, the reset module compares the strength of
Adaptive_resonance_theory
Branch of mathematics
R-Mod the category of left R-modules and by Mod-R the category of right R-modules (if R is commutative, the two categories coincide). Fix a module B in R-Mod
Homological_algebra
{\displaystyle H^{*}(X;\mathbb {Z} /p)} . In particular, it gives the structure of a module over the Steenrod algebra A p {\displaystyle {\mathcal {A}}_{p}} for H ∗
Eilenberg–MacLane_spectrum
Open source module tracker
MOD Plugin, which enabled users to play music and other sounds encoded in module files. ModPlug Tracker, along with a player application named ModPlug Player
OpenMPT
British mathematician
1112/jlms/s2-43.1.37. MR 1099084. Rickard, Jeremy (1997). "Idempotent modules in the stable category". Journal of the London Mathematical Society. Second Series
Jeremy_Rickard
History of maths
This is a timeline of category theory and related mathematics. Its scope ("related mathematics") is taken as: Categories of abstract algebraic structures
Timeline of category theory and related mathematics
Timeline_of_category_theory_and_related_mathematics
Music tracker and modular synthesizer developed by Alexander "NightRadio" Zolotov
in SunVox). MetaModule is notable in this category because this loads another SunVox project within the current project as a module, which is useful
SunVox
Tools for studying groups based on techniques from algebraic topology
each module M {\displaystyle M} to the group of invariants M G {\displaystyle M^{G}} yields a functor from the category of G {\displaystyle G} -modules to
Group_cohomology
Sling used for swinging, sleeping or resting
program, from Apollo 12 onwards, the Lunar Module was equipped with hammocks for the commander and lunar module pilot to sleep in between moonwalks. In Mexico
Hammock
Generalisation of a sheaf; a fibered category that admits effective descent
category of quasi-coherent sheaves as the Lis-Et topology, but has a subtle problem: the natural embedding of quasi-coherent sheaves into OX modules in
Stack_(mathematics)
Region of non-coding DNA that regulates the transcription of neighboring genes
Cis-regulatory elements (CREs) or cis-regulatory modules (CRMs) are regions of non-coding DNA which regulate the transcription of neighboring genes. CREs
Cis-regulatory_element
Terpene hydrocarbon
peel waste, (+)-limonene is typically removed. Limonene is a relatively stable monoterpene and can be distilled without decomposition, although at elevated
Limonene
Free software music tracker
for composing music in the MOD and XM module file formats. It is a clone that attempts to recreate the module replay and user experience of the popular
MilkyTracker
Medical classification created by the World Health Organisation (WHO)
updates to be made without having to change the other categories, ensuring that codes remain stable. The ICD-11 features five new chapters. The third chapter
ICD-11
Vehicle safety device
It consists of an airbag cushion, a flexible fabric bag, an inflation module, and an impact sensor. The purpose of the airbag is to provide a vehicle
Airbag
Programming language
When compiled just in time, Dart code produces performant modules that compile fast. This module needs the Dart VM included with the SDK to run. The compiler
Dart_(programming_language)
Concept in algebra
the K-theory is a 'universal additive invariant' of dg-categories and small stable ∞-categories. The motivation for this notion comes from algebraic K-theory
K-theory_of_a_category
Free Unix-like operating system kernel
userspace programs that rely on them. Loadable kernel modules (LKMs), by design, cannot rely on a stable ABI. Therefore, they must always be recompiled whenever
Linux_kernel
Free and open-source disk encryption utility
to the computer. VeraCrypt does not take advantage of Trusted Platform Module (TPM). VeraCrypt FAQ repeats the negative opinion of the original TrueCrypt
VeraCrypt
Branch of mathematics that studies abstract algebraic structures
their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essence, a representation
Representation_theory
A} -module, then the category of comodules Comod ( A , Γ ) {\displaystyle {\text{Comod}}(A,\Gamma )} of the Hopf-algebroid is an abelian category. There
Comodule over a Hopf algebroid
Comodule_over_a_Hopf_algebroid
Releases of Debian GNU/Linux, a computer operating system
When the Debian stable branch is replaced with a newer release, the current stable becomes an "oldstable" release. When the Debian stable branch is replaced
Debian release version history
Debian_release_version_history
Programmable digital computer used to control machinery
maintenance than relay systems. It was easily expandable with additional I/O modules. While relay systems required tedious and sometimes complicated hardware
Programmable_logic_controller
Type of solar power cell
Mining byproducts can be converted into a stable CdTe compound and safely encapsulated inside CdTe PV solar modules for years. A large growth in the CdTe
Cadmium telluride photovoltaics
Cadmium_telluride_photovoltaics
Unit testing framework module
CppUnit is a unit testing framework module for the C++ programming language. It allows unit-testing of C sources as well as C++ with minimal source modification
CppUnit
Self-stable region of a protein's chain that folds independently from the rest
calcium-binding EF hand domain of calmodulin. Because they are independently stable, domains can be "swapped" by genetic engineering between one protein and
Protein_domain
Spacecraft thrusters used to provide attitude control and translation
attitude control, rather than RCS. Use of diverted engine thrust to provide stable attitude control of a short-or-vertical takeoff and landing aircraft below
Reaction_control_system
Computer code templating system
compatible with ASCII. Haml can be used at the command line, as a separate Ruby module, or in a Ruby on Rails application. Haml was originally introduced by Hampton
Haml
Computer storage device with no moving parts
5-inch or 1.8-inch) and not the dimensions of the drive casing. A disk-on-a-module (DOM) is a flash drive with either 40/44-pin Parallel ATA (PATA) or SATA
Solid-state_drive
Data structure for approximate set membership
PMC 6304992. PMID 30509984. Maggs & Sitaraman (2015). "Bloom index contrib module". Postgresql.org. 2016-04-01. Archived from the original on 2018-09-09.
Bloom_filter
Subject area in mathematics
exact category, a category satisfying certain formal properties similar to, but slightly weaker than, the properties satisfied by a category of modules or
Algebraic_K-theory
Technique for the generative modeling of a continuous probability distribution
as Stable Diffusion and DALL-E. These models typically combine diffusion models with other models, such as text-encoders and cross-attention modules to
Diffusion_model
Indian crewed orbital spacecraft
Limited (HAL)-manufactured crew module underwent its first uncrewed experimental flight in 2014; design of the crew module was completed in 2019. The Defence
Gaganyaan
Anime-focused imageboard website
NovelAI, an AI image generation platform, uses a custom version of the Stable Diffusion text-to-image diffusion model called NovelAI Diffusion, which
Danbooru
Open-source PDF utility software
PDFsam Basic 3.3.2 with merge PDF module opened Developer Andrea Vacondio Initial release June 29, 2008 (2008-06-29) Stable release 6.0.1 / 1 May 2026; 44
PDF_Split_and_Merge
with coefficients in a crossed module, or a Picard category Johnson, Niles; Osorno, Angélica M. (2012). "Modeling Stable One-Types". arXiv:1201.2686 [math
Abelian_2-group
Supply chain management for transportation operations
A transportation management system (TMS) is a category of logistics software used to plan, execute, and optimize the movement of goods across supply chains
Transportation management system
Transportation_management_system
Solution concept for non-cooperative games
Mertens provided several formal definitions depending on the coefficient module used for homology or cohomology. A formal definition requires some notation
Mertens-stable_equilibrium
STABLE MODULE-CATEGORY
STABLE MODULE-CATEGORY
Boy/Male
Hindu
Stable
Surname or Lastname
English
English : variant of Staple.
Female
English
Feminine variant spelling of English unisex Stacey, STACEE means "resurrection."
Boy/Male
Vietnamese
Stable.
Surname or Lastname
English
English : topographic name for someone who lived by a stable, or an occupational name for someone employed in one, from Middle English stable, plural stables (via Old French from Latin stabulum, a derivative of stare ‘to stand’). In Middle English the term was used of the quarters occupied by cattle as well as those reserved for horses.
Boy/Male
Shakespearean American English
Henry VI, Part 2' Sir John Stanley. 'King Henry the Sixth, Part III' Sir William Stanley. 'King...
Boy/Male
Tamil
Stable
Female
English
Feminine variant spelling of English unisex Stacey, STACIE means "resurrection."
Surname or Lastname
English
English : topographic name for someone who lived near a boundary post, from Middle English stapel ‘post’ + the suffix -er, denoting an inhabitant.
Surname or Lastname
English, Dutch, North German, and Danish
English, Dutch, North German, and Danish : variant of Stubbe.
Surname or Lastname
English, North German, and Dutch
English, North German, and Dutch : from Old English stub(b), Middle Low German, Middle Dutch stubbe ‘tree stump’ or ‘tree trunk’, hence a topographic name for someone who lived on newly cleared land, or a nickname for a short, stout man.
Male
French
French name derived from Latin amabilis, AMABLE means "lovable."
Female
English
Variant spelling of English Mabel, MABLE means "lovable."Â
Female
English
English name derived from the vocabulary word, SABLE means "black," as a heraldic color. It is sometimes confused with the mammal of the same name but which has brown fur, not black, and which has a different origin.
Surname or Lastname
English
English : occupational name for someone who looked after horses or cattle, from an agent derivative of Middle English stable ‘stable’.German (Stäbler) : occupational name for an official who carried a staff as a symbol of office, Middle High German stebelære.
Female
English
Elaborated form of English Star, STARLA means "star."
Boy/Male
Indian, Sanskrit
Stable
Surname or Lastname
English
English : variant of Mule.
Surname or Lastname
English
English : from Middle English stapel ‘post’, hence a topographic name for someone who lived near a boundary post, or a habitational name from some place named with this word (Old English stapel), as for example Staple in Kent or Staple Fitzpaine in Somerset.Americanized spelling of German Stapel.
Surname or Lastname
English (Devon and Cornwall)
English (Devon and Cornwall) : habitational name from Scoble in Devon.
STABLE MODULE-CATEGORY
STABLE MODULE-CATEGORY
Girl/Female
Indian, Telugu
Part of Goddess Laxmi
Boy/Male
Indian, Punjabi, Sikh
One Remembering God
Girl/Female
Tamil
Look, Blessed with beauty, Shape, Beauty
Boy/Male
Norse
Supported Flosi.
Boy/Male
Hindu
Born of mind
Female
Greek
(Λήδα) Greek name LEDA means "woman." In mythology, this is the name of the mother of Kastor, Pollux and Helen.
Boy/Male
Tamil
Girl/Female
Muslim/Islamic
Brilliance
Boy/Male
Hindu, Indian, Marathi
Shiva
Surname or Lastname
English (Northumberland)
English (Northumberland) : habitational name from a place in Northumbria, so called from a British river name akin to Welsh arian ‘silvery’, ‘bright’ + Old English tūn ‘enclosure’, ‘settlement’.
STABLE MODULE-CATEGORY
STABLE MODULE-CATEGORY
STABLE MODULE-CATEGORY
STABLE MODULE-CATEGORY
STABLE MODULE-CATEGORY
a.
Pertaining to, or being market of staple for, commodities; as, a staple town.
a.
Not stable; not standing fast or firm; unstable; prone to change or recede from a purpose; mutable; inconstant.
v. i.
A house, shed, or building, for beasts to lodge and feed in; esp., a building or apartment with stalls, for horses; as, a horse stable; a cow stable.
a.
Suitable to be taken as a model or pattern; as, a model house; a model husband.
v. t.
To sort according to its staple; as, to staple cotton.
n.
A stable keeper.
v. t.
To put or keep in a stable.
a.
Of or pertaining to mode, modulation, module, or modius; as, modular arrangement; modular accent; modular measure.
v. t.
To form into a table or catalogue; to tabulate; as, to table fines.
a.
Liable to, or subjected by law to, taxation; as, ratable estate.
n.
The fiber of wool, cotton, flax, or the like; as, a coarse staple; a fine staple; a long or short staple.
pl.
of Modulus
v. i.
Firmly established; not easily moved, shaken, or overthrown; fixed; as, a stable government.
a.
Being of reasonable or suitable size; as, sizable timber; sizable bulk.
v. i.
Durable; not subject to overthrow or change; firm; as, a stable foundation; a stable position.
n.
To model; also, to modulate.
imp. & p. p.
of Stable
v. i.
To dwell or lodge in a stable; to dwell in an inclosed place; to kennel.
n.
A model or measure.
adv.
In a stable manner; firmly; fixedly; steadily; as, a government stably settled.