AI & ChatGPT searches , social queries for STRING DIAGRAM
Search references for STRING DIAGRAM. Phrases containing STRING DIAGRAM
See searches and references containing STRING DIAGRAM!
Search references for STRING DIAGRAM. Phrases containing STRING DIAGRAM
See searches and references containing STRING DIAGRAM!STRING DIAGRAM
Graphical representation of a morphism
In mathematics, string diagrams are a formal graphical language for representing morphisms in monoidal categories, or more generally 2-cells in 2-categories
String_diagram
Most general completion of a commutative square given two morphisms with same codomain
fibre product, fibered product or Cartesian square) is the limit of a diagram consisting of two morphisms f : X → Z and g : Y → Z with a common codomain
Pullback_(category_theory)
Diagram that shows all possible logical relations between a collection of sets
diagram is a widely used diagram style that shows the logical relation between sets, popularized by John Venn (1834–1923) in the 1880s. The diagrams are
Venn_diagram
Theorem in category theory
Higher-dimensional algebra Homotopy hypothesis Model category Simplex category String diagram n-categories Weak n-categories Bicategory (pseudofunctor) Tricategory
Lawvere's_fixed-point_theorem
General theory of mathematical structures
among morphisms (such as fg = h) are often depicted using commutative diagrams, with "points" (corners) representing objects and "arrows" representing
Category_theory
Collection of maps which give the same result
especially in category theory, a commutative diagram is a diagram such that all directed paths in the diagram with the same start and endpoints lead to the
Commutative_diagram
Mathematical concept
category C {\displaystyle C} are defined by means of diagrams in C {\displaystyle C} . Formally, a diagram of shape J {\displaystyle J} in C {\displaystyle
Limit_(category_theory)
Mapping between categories
{\displaystyle F} transforms each commutative diagram in C {\displaystyle C} into a commutative diagram in D {\displaystyle D} ; if f {\displaystyle f}
Functor
Embedding of categories into functor categories
is a natural transformation, we have the following commutative diagram: This diagram shows that the natural transformation Φ {\displaystyle \Phi } is
Yoneda_lemma
Indexed collection of objects and morphisms in a category
In category theory, a branch of mathematics, a diagram is the categorical analogue of an indexed family in set theory. The primary difference is that
Diagram_(category_theory)
Graphical language for quantum processes
linear maps between qubits, which are represented as string diagrams called ZX-diagrams. A ZX-diagram consists of a set of generators called spiders that
ZX-calculus
Construction in category theory
appearances in category theory as well. Let F : J → C be a diagram in C. Formally, a diagram is nothing more than a functor from J to C. The change in
Cone_(category_theory)
Set of arguments where two or more functions have the same value
objects and morphisms form a diagram in the category in question, and the equaliser is simply the limit of that diagram. In more explicit terms, the equaliser
Equaliser_(mathematics)
Applications of category theory
quantum mechanics ZX-calculus DisCoCat Petri net Univalent foundations String diagrams Journals: Compositionality Conferences: Applied category theory Symposium
Applied_category_theory
Category theory concept
the category C {\displaystyle {\mathcal {C}}} such that the following diagram commutes A → f A ′ π ↓ ↓ π ′ X = X {\displaystyle {\begin{matrix}A&\xrightarrow
Overcategory
Generalization of category
a double category. n-category Doctrine (mathematics) Pseudofunctor String diagram 2-Yoneda lemma Pasting theorem Ehresmann 2004 Ehresmann 1965 Bénabou
2-category
Category whose objects are sets and whose morphisms are functions
Higher-dimensional algebra Homotopy hypothesis Model category Simplex category String diagram n-categories Weak n-categories Bicategory (pseudofunctor) Tricategory
Category_of_sets
Special objects used in (mathematical) category theory
indeed the limit of the discrete diagram {Xi}, in general). Dually, an initial object is a colimit of the empty diagram 0 → C and can be thought of as an
Initial_and_terminal_objects
Quantum computing applied to natural language processing
categorical quantum mechanics and the DisCoCat framework, making use of string diagrams to translate from grammatical structure to quantum processes. The first
Quantum natural language processing
Quantum_natural_language_processing
In mathematics, invertible homomorphism
Higher-dimensional algebra Homotopy hypothesis Model category Simplex category String diagram n-categories Weak n-categories Bicategory (pseudofunctor) Tricategory
Isomorphism
Characterizing property of mathematical constructions
h:A\to A'} in C {\displaystyle {\mathcal {C}}} such that the following diagram commutes: We can dualize this categorical concept. A universal morphism
Universal_property
Map (arrow) between two objects of a category
functions. The composition of morphisms is often represented by a commutative diagram. For example, The collection of all morphisms from X {\displaystyle X}
Morphism
Category-theoretic construction
f_{2}=f\circ i_{2}.} That is, the following diagram commutes: The unique arrow f {\displaystyle f} making this diagram commute may be denoted f 1 ⊔ f 2 , {\displaystyle
Coproduct
Type of category in mathematics
Higher-dimensional algebra Homotopy hypothesis Model category Simplex category String diagram n-categories Weak n-categories Bicategory (pseudofunctor) Tricategory
Elementary_topos
Mathematical framework for natural language processing
word vectors to produce the meaning of a sentence or a piece of text. String diagrams are used to visualise information flow and reason about natural language
DisCoCat
Quotient space of a codomain of a linear map by the map's image
a morphism q : Y → Q such that the diagram commutes. Moreover, the morphism q must be universal for this diagram, i.e. any other such q′ : Y → Q′ can
Cokernel
Category theory constructs
the natural transformation ϵ {\displaystyle \epsilon } in the following diagram: Formally, the right Kan extension of X {\displaystyle X} along F {\displaystyle
Kan_extension
Higher-dimensional algebra Homotopy hypothesis Model category Simplex category String diagram n-categories Weak n-categories Bicategory (pseudofunctor) Tricategory
3-category
Collection of objects and morphisms
{\displaystyle fg=h} ) can most conveniently be represented with commutative diagrams, where the objects are represented as points and the morphisms as arrows
Category_(mathematics)
Type of category in mathematics
Higher-dimensional algebra Homotopy hypothesis Model category Simplex category String diagram n-categories Weak n-categories Bicategory (pseudofunctor) Tricategory
Topos
Higher-dimensional algebra Homotopy hypothesis Model category Simplex category String diagram n-categories Weak n-categories Bicategory (pseudofunctor) Tricategory
Lift_(mathematics)
Category theory
Higher-dimensional algebra Homotopy hypothesis Model category Simplex category String diagram n-categories Weak n-categories Bicategory (pseudofunctor) Tricategory
Kleisli_category
Category admitting tensor products
subject to certain coherence conditions, which ensure that all the relevant diagrams commute. The ordinary tensor product makes vector spaces, abelian groups
Monoidal_category
Central object of study in category theory
commutative diagram: If both F {\displaystyle F} and G {\displaystyle G} are instead contravariant functors, the vertical arrows in the right diagram are reversed
Natural_transformation
Most general completion of a commutative square given two morphisms with same domain
fibered sum or cocartesian square or amalgamated sum) is the colimit of a diagram consisting of two morphisms f : Z → X and g : Z → Y with a common domain
Pushout_(category_theory)
Category equipped with a faithful functor to the category of sets
Higher-dimensional algebra Homotopy hypothesis Model category Simplex category String diagram n-categories Weak n-categories Bicategory (pseudofunctor) Tricategory
Concrete_category
Higher-dimensional algebra Homotopy hypothesis Model category Simplex category String diagram n-categories Weak n-categories Bicategory (pseudofunctor) Tricategory
Refinement_(category_theory)
Concept in mathematics
Higher-dimensional algebra Homotopy hypothesis Model category Simplex category String diagram n-categories Weak n-categories Bicategory (pseudofunctor) Tricategory
Tensor–hom_adjunction
t : A × B → B, there exists a unique f : LA → B such that the following diagram commutes: where〈idA, f〉denotes the arrow induced by the universal property
List_object
Aspect of category theory
construction dual to the equalizer. A coequalizer is the colimit of a diagram consisting of two objects X and Y and two parallel morphisms f, g : X →
Coequalizer
Correspondence between properties of a category and its opposite
Higher-dimensional algebra Homotopy hypothesis Model category Simplex category String diagram n-categories Weak n-categories Bicategory (pseudofunctor) Tricategory
Dual_(category_theory)
Concept in mathematical category theory
such that the following diagrams commute: The unit coherence: The associativity coherence: The inverse law: In the diagrams above, a, l, and r are the
Symmetric_monoidal_category
Functors which are surjective and injective on hom-sets
Higher-dimensional algebra Homotopy hypothesis Model category Simplex category String diagram n-categories Weak n-categories Bicategory (pseudofunctor) Tricategory
Full_and_faithful_functors
Concept in category theory
Higher-dimensional algebra Homotopy hypothesis Model category Simplex category String diagram n-categories Weak n-categories Bicategory (pseudofunctor) Tricategory
Forgetful_functor
Relationship between two functors abstracting many common constructions
the zig-zag equations because of the appearance of the corresponding string diagrams. A way to remember them is to first write down the nonsensical equation
Adjoint_functors
Category whose objects and morphisms are inside a bigger category
Higher-dimensional algebra Homotopy hypothesis Model category Simplex category String diagram n-categories Weak n-categories Bicategory (pseudofunctor) Tricategory
Subcategory
Product of two categories, in category theory
Higher-dimensional algebra Homotopy hypothesis Model category Simplex category String diagram n-categories Weak n-categories Bicategory (pseudofunctor) Tricategory
Product_category
Generalized object in category theory
× X 2 {\displaystyle f:Y\to X_{1}\times X_{2}} such that the following diagram commutes: Whether a product exists may depend on C {\displaystyle C} or
Product_(category_theory)
Functor type
Higher-dimensional algebra Homotopy hypothesis Model category Simplex category String diagram n-categories Weak n-categories Bicategory (pseudofunctor) Tricategory
Representable_functor
Category with direct sums and certain types of kernels and cokernels
Higher-dimensional algebra Homotopy hypothesis Model category Simplex category String diagram n-categories Weak n-categories Bicategory (pseudofunctor) Tricategory
Abelian_category
Mathematical concept
\mathbf {C} } is small, the end can be described as the equalizer in the diagram ∫ c S ( c , c ) → ∏ c ∈ C S ( c , c ) ⇉ ∏ c → c ′ S ( c , c ′ ) , {\displaystyle
End_(category_theory)
Generalization of category theory
Higher-dimensional algebra Homotopy hypothesis Model category Simplex category String diagram n-categories Weak n-categories Bicategory (pseudofunctor) Tricategory
Higher_category_theory
Injective homomorphism
Higher-dimensional algebra Homotopy hypothesis Model category Simplex category String diagram n-categories Weak n-categories Bicategory (pseudofunctor) Tricategory
Monomorphism
Relation of categories in category theory
Higher-dimensional algebra Homotopy hypothesis Model category Simplex category String diagram n-categories Weak n-categories Bicategory (pseudofunctor) Tricategory
Isomorphism_of_categories
Higher-dimensional algebra Homotopy hypothesis Model category Simplex category String diagram n-categories Weak n-categories Bicategory (pseudofunctor) Tricategory
Fundamental_groupoid
Higher-dimensional algebra Homotopy hypothesis Model category Simplex category String diagram n-categories Weak n-categories Bicategory (pseudofunctor) Tricategory
Localization_of_a_category
Higher category theory concept
Higher-dimensional algebra Homotopy hypothesis Model category Simplex category String diagram n-categories Weak n-categories Bicategory (pseudofunctor) Tricategory
Weak_n-category
Categorical procedure
The skeletonization of fusion categories is often stated in terms of string diagrams. In this approach, morphims in the category are depicted as strings
Skeletonization of fusion categories
Skeletonization_of_fusion_categories
Type of category in category theory
product, is a final object and the empty product in the case of an empty diagram, an initial object. Both being limits, they are not finite products nor
Additive_category
Construction in category theory
such pair (Y, ψi) there exists a unique morphism u: Y → X such that the diagram commutes for all i ≤ j. The inverse limit is often denoted X = lim ←
Inverse_limit
Visualization of string instrument fingering
a chord diagram (also called a fretboard diagram or fingering diagram) is a diagram indicating the fingering of a chord on fretted string instruments
Chord_diagram_(music)
In mathematics, collection of classes
Higher-dimensional algebra Homotopy hypothesis Model category Simplex category String diagram n-categories Weak n-categories Bicategory (pseudofunctor) Tricategory
Conglomerate_(mathematics)
Special case of colimit in category theory
i {\displaystyle u\circ \phi _{i}=\psi _{i}} for each i. The following diagram will then commute for all i, j. The direct limit is often denoted X = lim
Direct_limit
Endofunctor on the category V of finite-dimensional vector spaces
Higher-dimensional algebra Homotopy hypothesis Model category Simplex category String diagram n-categories Weak n-categories Bicategory (pseudofunctor) Tricategory
Polynomial_functor
Categorical generalization of a function space in set theory
(called the transpose of g {\displaystyle g} ) such that the following diagram commutes: This assignment of a unique λ g {\displaystyle \lambda g} to
Exponential_object
Generalization of the kernel of a homomorphism
Higher-dimensional algebra Homotopy hypothesis Model category Simplex category String diagram n-categories Weak n-categories Bicategory (pseudofunctor) Tricategory
Kernel_(category_theory)
Connects set theory with category theory
Higher-dimensional algebra Homotopy hypothesis Model category Simplex category String diagram n-categories Weak n-categories Bicategory (pseudofunctor) Tricategory
Categorification
Computing company founded in 2014
task-specific output. This is encoded into an abstract representation called a string diagram, which reflects the relationships between the words in the original
Quantinuum
Aspect of category theory in mathematics
Higher-dimensional algebra Homotopy hypothesis Model category Simplex category String diagram n-categories Weak n-categories Bicategory (pseudofunctor) Tricategory
Rig_category
Monoidal category
Higher-dimensional algebra Homotopy hypothesis Model category Simplex category String diagram n-categories Weak n-categories Bicategory (pseudofunctor) Tricategory
Tannakian_formalism
Mathematical construction used in homotopy theory
given by functors N: sAb → Ch+ and Γ: Ch+ → sAb. See also: simplicial diagram. Simplicial sets were originally used to give precise and convenient descriptions
Simplicial_set
Type of category in category theory
Higher-dimensional algebra Homotopy hypothesis Model category Simplex category String diagram n-categories Weak n-categories Bicategory (pseudofunctor) Tricategory
Cartesian_closed_category
Concept in category theory
braidings denoted γ {\displaystyle \gamma } ) such that the following diagram commutes for every pair of objects A, B in C {\displaystyle {\mathcal {C}}}
Monoidal_functor
Mathematical category formed by reversing morphisms
Higher-dimensional algebra Homotopy hypothesis Model category Simplex category String diagram n-categories Weak n-categories Bicategory (pseudofunctor) Tricategory
Opposite_category
Abstract mathematics relationship
Higher-dimensional algebra Homotopy hypothesis Model category Simplex category String diagram n-categories Weak n-categories Bicategory (pseudofunctor) Tricategory
Equivalence_of_categories
Mathematics construct
B {\displaystyle {\mathcal {B}}} respectively, such that the following diagram commutes: Morphisms are composed by taking ( f ′ , g ′ ) ∘ ( f , g ) {\displaystyle
Comma_category
Type of quotient object in mathematics
Higher-dimensional algebra Homotopy hypothesis Model category Simplex category String diagram n-categories Weak n-categories Bicategory (pseudofunctor) Tricategory
Quotient_category
Hypothesis in mathematical category theory
Higher-dimensional algebra Homotopy hypothesis Model category Simplex category String diagram n-categories Weak n-categories Bicategory (pseudofunctor) Tricategory
Homotopy_hypothesis
Abstract homotopical model for topological spaces
Higher-dimensional algebra Homotopy hypothesis Model category Simplex category String diagram n-categories Weak n-categories Bicategory (pseudofunctor) Tricategory
∞-groupoid
Higher categorical generalization of a topos
Higher-dimensional algebra Homotopy hypothesis Model category Simplex category String diagram n-categories Weak n-categories Bicategory (pseudofunctor) Tricategory
∞-topos
Higher-dimensional algebra Homotopy hypothesis Model category Simplex category String diagram n-categories Weak n-categories Bicategory (pseudofunctor) Tricategory
Tetracategory
Category in which all small limits exist
which all small limits exist. That is, a category C is complete if every diagram F : J → C (where J is small) has a limit in C. Dually, a cocomplete category
Complete_category
Category whose hom objects correspond (di-)naturally to objects in itself
Higher-dimensional algebra Homotopy hypothesis Model category Simplex category String diagram n-categories Weak n-categories Bicategory (pseudofunctor) Tricategory
Closed_category
Bi-universal property in category theory
objects X, Y, Z in C and all morphisms f : Y → Z, g : X → Y, the following diagram commutes: The morphisms 0XY necessarily are zero morphisms and form a compatible
Zero_morphism
Functor that preserves short exact sequences
Higher-dimensional algebra Homotopy hypothesis Model category Simplex category String diagram n-categories Weak n-categories Bicategory (pseudofunctor) Tricategory
Exact_functor
Object in category theory
∘ s = f ∘ u. In other words, the triangle and square in the following diagram commute. The pair (q, f) is sometimes called the recursion data for u,
Natural_numbers_object
Homological construction in category theory
are "natural" in several technical senses. First, given a commutative diagram of the form 0 → A 1 → f 1 B 1 → g 1 C 1 → 0 α ↓ β ↓ γ ↓ 0 → A 2 → f 2 B
Derived_functor
Category of non-empty finite ordinals and order-preserving maps
Higher-dimensional algebra Homotopy hypothesis Model category Simplex category String diagram n-categories Weak n-categories Bicategory (pseudofunctor) Tricategory
Simplex_category
Higher-dimensional algebra Homotopy hypothesis Model category Simplex category String diagram n-categories Weak n-categories Bicategory (pseudofunctor) Tricategory
Stable_∞-category
Concept in category theory
Higher-dimensional algebra Homotopy hypothesis Model category Simplex category String diagram n-categories Weak n-categories Bicategory (pseudofunctor) Tricategory
Point-surjective_morphism
Mathematical category whose hom sets form Abelian groups
Higher-dimensional algebra Homotopy hypothesis Model category Simplex category String diagram n-categories Weak n-categories Bicategory (pseudofunctor) Tricategory
Preadditive_category
a unique functor F' : C(G) → D such that U(F')∘I=F, i.e. the following diagram commutes: The functor C is left adjoint to the forgetful functor U. Mathematics
Free_category
Category enriched over the category of simplicial sets
Higher-dimensional algebra Homotopy hypothesis Model category Simplex category String diagram n-categories Weak n-categories Bicategory (pseudofunctor) Tricategory
Simplicially enriched category
Simplicially_enriched_category
Surjective homomorphism
Higher-dimensional algebra Homotopy hypothesis Model category Simplex category String diagram n-categories Weak n-categories Bicategory (pseudofunctor) Tricategory
Epimorphism
Category whose objects are R-modules and whose morphisms are module homomorphisms
Higher-dimensional algebra Homotopy hypothesis Model category Simplex category String diagram n-categories Weak n-categories Bicategory (pseudofunctor) Tricategory
Category_of_modules
Category whose objects are sets and whose morphisms are binary relations
Higher-dimensional algebra Homotopy hypothesis Model category Simplex category String diagram n-categories Weak n-categories Bicategory (pseudofunctor) Tricategory
Category_of_relations
Study of categorified structures
Higher-dimensional algebra Homotopy hypothesis Model category Simplex category String diagram n-categories Weak n-categories Bicategory (pseudofunctor) Tricategory
Higher-dimensional_algebra
Pictorial representation of the behavior of subatomic particles
In theoretical physics, a Feynman diagram is a pictorial representation of the mathematical expressions describing the behavior and interaction of subatomic
Feynman_diagram
Symmetric monoidal infinity category
Higher-dimensional algebra Homotopy hypothesis Model category Simplex category String diagram n-categories Weak n-categories Bicategory (pseudofunctor) Tricategory
En-ring
Higher-dimensional algebra Homotopy hypothesis Model category Simplex category String diagram n-categories Weak n-categories Bicategory (pseudofunctor) Tricategory
Essentially surjective functor
Essentially_surjective_functor
travel, tourism, insurance
STRING DIAGRAM
STRING DIAGRAM
STRING DIAGRAM
STRING DIAGRAM
STRING DIAGRAM
STRING DIAGRAM
STRING DIAGRAM
STRING DIAGRAM
STRING DIAGRAM
travel, tourism, insurance