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Mathematical concept
Univalent foundations are an approach to the foundations of mathematics in which mathematical structures are built out of objects called types. Types
Univalent_foundations
Topics referred to by the same term
Univalent may refer to: Univalent function – an injective holomorphic function on an open subset of the complex plane Univalent foundations – a type-based
Univalent
Mathematical concept
plane is called univalent if it is injective. The function f : z ↦ 2 z + z 2 {\displaystyle f\colon z\mapsto 2z+z^{2}} is univalent in the open unit
Univalent_function
Type theory in logic and mathematics
between the work referred to as homotopy type theory, and that called the univalent foundations project. Although neither is precisely delineated, and the
Homotopy_type_theory
German professor of computer science
homotopy type theory. Altenkirch was part of the 2012/2013 special year on univalent foundations at the Institute for Advanced Study. At Nottingham he co-chairs
Thorsten_Altenkirch
Russian mathematician (1966–2017)
the Milnor conjecture and motivic Bloch–Kato conjectures and for the univalent foundations of mathematics and homotopy type theory. Vladimir Voevodsky's
Vladimir_Voevodsky
concerning holomorphic univalent functions defined on the unit disk in the complex numbers. The theorem states that a univalent function defined on the
Grunsky's_theorem
Proof compression algorithm
mathematical logic, LowerUnivalents is an algorithm used for the compression of propositional resolution proofs. LowerUnivalents is a generalised algorithm
LowerUnivalents
Typographic symbol
Wolfram MathWorld. Retrieved 2020-08-24. Univalent Foundations Program (2013). Homotopy Type Theory: Univalent Foundations of Mathematics (GitHub version)
Vertical_bar
Relationship between elements of two sets
1} to 0 {\displaystyle 0} ). Functional (also called right-unique or univalent): for all x ∈ X {\displaystyle x\in X} and all y , z ∈ Y , {\displaystyle
Binary_relation
Statement in complex analysis
2 z − 2 + ⋯ {\displaystyle g(z)=z+b_{1}z^{-1}+b_{2}z^{-2}+\cdots } is univalent in | z | > 1 {\displaystyle |z|>1} . Then ∑ n = 1 ∞ n | b n | 2 ≤ 1. {\displaystyle
Koebe_quarter_theorem
Matrix used in complex analysis
the univalent function itself. The Grunsky matrix and its associated inequalities were originally formulated in a more general setting of univalent functions
Grunsky_matrix
Combining capacity of elements with other atoms
the compound. Valence is defined by the IUPAC as: The maximum number of univalent atoms (originally hydrogen or chlorine atoms) that may combine with an
Valence_(chemistry)
Postgraduate center in New Jersey, US
format "Univalent Foundations of Mathematics – Events | Institute for Advanced Study". www.ias.edu. October 21, 2010. "Homotopy Type Theory: Univalent Foundations
Institute_for_Advanced_Study
Chemical compound
is also the class of compounds containing this ring. Isoxazolyl is the univalent functional group derived from isoxazole. Isoxazole rings are found in
Isoxazole
American mathematician
mathematician who contributed to number theory, graph theory and to the theory of univalent functions: The conjecture on the coefficients of multivalent functions
Adolph_Winkler_Goodman
Family of double sulfate salts of aluminium
the alums, which are dodecahydrates, double sulfates and selenates of univalent and trivalent cations occur with other degrees of hydration. These materials
Alum
Characterization of starlike univalent holomorphic functions
holomorphic univalent functions on the unit disk which are starlike. Nevanlinna used this criterion to prove the Bieberbach conjecture for starlike univalent functions
Nevanlinna's_criterion
Mathematical theorem
of univalent holomorphic functions on an open domain has a uniform limit on compacta, then either the limit is constant or the limit is univalent. If
Riemann_mapping_theorem
British mathematician (1926–2020)
Editrice, pp. 119–125, MR 1249093, Zbl 0851.42009. Hayman, W. K. (2002), "Univalent and Multivalent Functions", in Kuhnau, Reiner (ed.), Geometric Function
Walter_Hayman
Nonlinear differential operator used to study conformal mappings
hypergeometric functions. It plays an important role in the theory of univalent functions, conformal mapping and Teichmüller spaces. It is named after
Schwarzian_derivative
Theorem in complex analysis
of Carathéodory's results on prime ends and the boundary behaviour of univalent holomorphic functions. The first proof of Carathéodory's theorem presented
Carathéodory's theorem (conformal mapping)
Carathéodory's_theorem_(conformal_mapping)
Logic principle
equality Type theory Univalence axiom The Univalent Foundations Program (2013). Homotopy Type Theory: Univalent Foundations of Mathematics. Princeton, NJ:
Extensionality
Anticoagulant medication taken by mouth
(hirudin and analogs) bind both to the active site and exosite 1, while univalent DTIs bind only to the active site. The third class of inhibitors, which
Direct_thrombin_inhibitor
American mathematician (born 1980)
Special Year on Univalent Foundations of Mathematics. Shulman was one of the principal authors of the book Homotopy type theory: Univalent foundations of
Michael Shulman (mathematician)
Michael_Shulman_(mathematician)
Branch of mathematics that studies sets
nLab Homotopy Type Theory: Univalent Foundations of Mathematics Archived 2021-01-22 at the Wayback Machine. The Univalent Foundations Program. Institute
Set_theory
Topics referred to by the same term
type, or function related to a monad (functional programming) Monadic or univalent, a chemical valence Monadic, in theology, a religion or philosophy possessing
Monadic
Results on triad homotopy groups
Theory, Homotopy Theory and Univalent Foundations)". 2013. The Univalent Foundations Program (2013). Homotopy type theory: Univalent foundations of mathematics
Blakers–Massey_theorem
Mathematician specializing in complex analysis and differential equations
February 1915 – 1978) was a mathematician who worked on Complex Analysis, Univalent Functions Theory, and Differential and Integral Equations. He was a student
Zeev_Nehari
Ordinary differential equation
generalizes the notion of a univalent semigroup. The Loewner differential equation has led to inequalities for univalent functions that played an important
Loewner_differential_equation
Statement in complex analysis; formerly the Bieberbach conjecture
statement concerns the Taylor coefficients a n {\displaystyle a_{n}} of a univalent function, i.e., a one-to-one holomorphic function that maps the unit disk
De_Branges's_theorem
chromosome pairs (bivalents) or single chromosomes without mating partners (univalents), or even whole sets of chromosomes, in that these are separated according
Non-random segregation of chromosomes
Non-random_segregation_of_chromosomes
Chemical group (–SO2–C6H4–CH3)
chemistry, a toluenesulfonyl group (tosyl group, abbreviated Ts or Tos) is a univalent functional group with the chemical formula −SO2−C6H4−CH3. It consists
Tosyl_group
Finnish mathematician (1925–2020)
Wissenschaften, 2nd edition: Quasiconformal mappings in the plane. Springer 1973. Univalent functions and Teichmüller Spaces. Springer, Graduate Texts in Mathematics
Olli_Lehto
Gabriel Koenigs, it gives a canonical representation as dilations of a univalent holomorphic mapping, or a semigroup of mappings, of the unit disk in the
Koenigs_function
Type of binary relation
xRaR^{T}yRbR^{T}z.} Since R is univalent, yRb and aRTy imply a=b. Therefore xRaRTz, hence xR;RTz and R;RT is transitive. Corollary: If R is univalent, then R;RT is an
Transitive_relation
nitrogen dioxide (NO2) moiety when it occurs in a larger compound as a univalent fragment. Examples include nitryl fluoride (NO2F) and nitryl chloride
Nitryl
become applicable to multiple different models. For example, reasoning in univalent foundations yields theorems about arbitrary (∞, 1)-toposes. Furthermore
Synthetic_mathematics
Mathematical theorem in real analysis
uses the terms 'simple' and 'schlicht' (function) in place of 'univalent'. Univalent means holomorphic and injective. James Munkres (1999). Topology
Uniform_limit_theorem
Simultaneous conflicting beliefs or feelings
validity affects how the interpretation is perceived. If a successful univalent attitude is achieved, final evaluations are labelled as either true or
Ambivalence
Arene complexes of univalent gallium, indium, and thallium are complexes featuring the centric (η6) coordination of the metal to the arene. Although arene
Arene complexes of univalent gallium, indium, and thallium
Arene_complexes_of_univalent_gallium,_indium,_and_thallium
seriously improved the known coefficient estimate for univalent functions. Milin’s monograph “Univalent functions and orthonormal systems” (1971) includes
Isaak_Moiseevich_Milin
Drug discovery
site and exosite 1 and act as competitive inhibitors of fibrin, while univalent DTIs block only the active site and can therefore both inhibit unbound
Discovery and development of direct thrombin inhibitors
Discovery_and_development_of_direct_thrombin_inhibitors
Study of space and shapes locally given by a convergent power series
holomorphic function on an open subset of the complex plane is called univalent if it is injective. One can prove that if G {\displaystyle G} and Ω {\displaystyle
Geometric_function_theory
Chemical element with atomic number 20 (Ca)
always divalent in its compounds, which are usually ionic. Hypothetical univalent salts of calcium would be stable with respect to their elements, but not
Calcium
Statement in complex analysis
the Fekete–Szegő inequality is an inequality for the coefficients of univalent analytic functions found by Fekete and Szegő (1933), related to the Bieberbach
Fekete–Szegő_inequality
Canadian mathematician
Advanced Study in 2013, where he was invited to join the Special Year on Univalent Foundations of Mathematics. He discovered Kripke–Joyal semantics, the
André_Joyal
The uniform convergence on compact sets of a sequence of holomorphic univalent functions, defined on the unit disk in the complex plane and fixing 0
Carathéodory_kernel_theorem
Logical system in mathematics
a flavor of type theory which gives a computational interpretation to univalent foundations (also known as homotopy type theory). In cubical type theory
Cubical_type_theory
In type theory, a type with no terms
both are denoted ⊥ {\displaystyle \bot } . Univalent Foundations Program (2013). Homotopy Type Theory: Univalent Foundations of Mathematics. Institute for
Empty_type
How spheres of various dimensions can wrap around each other
v226.n2.a2, S2CID 119303902. Homotopy type theory—univalent foundations of mathematics, The Univalent Foundations Program and Institute for Advanced Study
Homotopy_groups_of_spheres
Class of chemical compounds
whether or not further substituted in the phenyl ring by one or more other univalent substituents; (ii) by substitution at the 3-position with an alkyl substituent;
Substituted_cathinone
Toxic effects of thallium
thallium's high toxicity is that when present in aqueous solution as the univalent thallium(I) ion (Tl+) it exhibits some similarities with essential alkali
Thallium_poisoning
Reasoning about equations with free variables
is the identity on the domain of R. But a univalent relation is only a partial function, while a univalent total relation is a function. The formula for
Algebraic_logic
Mathematical term; concerning axioms used to derive theorems
eds. (11 November 2019). Reflections on the Foundations of Mathematics: Univalent Foundations, Set Theory and General Thoughts. Springer Nature. p. 177
Axiomatic_system
where P {\displaystyle P} is a polynomial and ϕ {\displaystyle \phi } is univalent. Goodman, A. W. (1948). "On some determinants related to 𝑝-valent functions"
Goodman's_conjecture
Superseded standard on quantities and units
hydrogen ion H+ and y1 denotes the activity coefficient of a typical uni-univalent electrolyte in the solution. Its definitions include: It included definitions
ISO_31
Electron in the outer shell of an atom's energy levels
Four covalent bonds. Carbon has four valence electrons and here a valence of four. Each hydrogen atom has one valence electron and is univalent.
Valence_electron
Mathematics award
Institute for Advanced Study, US "Major contributions in the primes, in univalent functions and the local Bieberbach conjecture, in theory of functions
Fields_Medal
Preparation for acquired immunity to disease
or antigens.[citation needed] Vaccines may be monovalent (also called univalent) or multivalent (also called polyvalent). A monovalent vaccine is designed
Vaccine
ISBN 978-3-939897-87-3. S2CID 15020752. Univalent Foundations Program (2013). Homotopy Type Theory: Univalent Foundations of Mathematics. Institute for
Polynomial functor (type theory)
Polynomial_functor_(type_theory)
Mathematical-logic system
Languages, p. 273, Benjamin C. Pierce "Scott's Representation Theorem and the Univalent Karoubi Envelope" (PDF). Dagstuhl Publishing. Retrieved 2026-05-19. Pierce
Lambda_calculus
American mathematician (1935–2020)
of H p {\displaystyle H^{p}} -Spaces, Academic Press, Dover 2000 1983: Univalent Functions, Grundlehren der mathematischen Wissenschaften, Springer Verlag
Peter_Duren
Process in geometric function theory
their boundary circles. This problem can be reduced to that of finding univalent holomorphic maps f, g of the unit disk and its complement into the extended
Conformal_welding
American mathematician
University Thesis The Inner Mapping Radius And Construction Of Harmonic, Univalent Mappings Of The Unit Disk (1997) Doctoral advisor Ted Joe Suffridge
Michael_Dorff
American architect (1939–2019)
postmodern architecture, claiming that modern architecture concentrates on univalent forms such as right angles and square buildings often resembling office
Charles_Jencks
Generalization of the real numbers
(paperback), ISBN 0-7456-3878-3 (hardcover). The Univalent Foundations Program (2013). Homotopy Type Theory: Univalent Foundations of Mathematics. Princeton, NJ:
Surreal_number
Amount of substance needed to fully react with a given amount of another
of a human is defined between 3.5 and 5.0 mEq/L. A certain amount of univalent ions provides the same amount of equivalents while the same amount of
Equivalent_(chemistry)
Hydrocarbon compound containing one or more C=C bonds
2420580122. PMC 12002291. PMID 40127274. Rule A-3. Unsaturated Compounds and Univalent Radicals IUPAC Blue Book. Rule A-4. Bivalent and Multivalent Radicals
Alkene
Addition, multiplication, division, ...
domain is that a relation that corresponds to a binary operation is a univalent relation. Hyperoperation Infix notation Operator (mathematics) Order of
Operation_(mathematics)
Chemical compound
group is a univalent radical C10H17 derived from borneol by removal of hydroxyl and is also known as 2-bornyl. Isobornyl is the univalent radical C10H17
Borneol
American mathematician
1090/S0002-9947-1974-0344468-7. Baernstein, Albert (1974). "Integral means, univalent functions and circular symmetrization". Acta Mathematica. 133 (1): 139–169
Albert_Baernstein_II
Relationship between programs and proofs
AI]. Baez & Stay 2011. Homotopy Type Theory: Univalent Foundations of Mathematics. (2013) The Univalent Foundations Program. Institute for Advanced Study
Curry–Howard_correspondence
Molecular substituent derived from cyclic monosaccharides
In organic chemistry, a glycosyl group is a univalent free radical or substituent structure obtained by removing the hydroxyl (−OH) group from the hemiacetal
Glycosyl
Mathematical theory of data types
doi:10.1007/BF00484985. ISSN 1573-0964. The Univalent Foundations Program (2013). Homotopy Type Theory: Univalent Foundations of Mathematics. Homotopy Type
Type_theory
Basic unit distinguishing one sound from another in a language
the existence of single-valued features. These features, called unary, univalent, or privative features, can only describe the classes of segments that
Distinctive_feature
Association of one output to each input
Sarikaya, Deniz (eds.). Reflections on the Foundations of Mathematics: Univalent Foundations, Set Theory and General Thoughts. Synthese Library. Vol. 407
Function_(mathematics)
states that there is a nonconstant single-valued holomorphic function (univalent function) on such a Riemann surface. It is a generalization of the Runge
Behnke–Stein theorem on Stein manifolds
Behnke–Stein_theorem_on_Stein_manifolds
Measure of the ability of a solution containing electrolytes to conduct electricity
Shedlovsky, Theodore (1932). "The Electrolytic Conductivity of some Uni-Univalent Electrolytes in Water at 25°". Journal of the American Chemical Society
Conductivity_(electrolytic)
Israeli sociologist and linguist
and the interrelationship of literary systems. Even-Zohar substitutes univalent causal parameters with polyvalent factors as an instrument for explaining
Itamar_Even-Zohar
not substituted in any of the linked sub-structures with one or more univalent substituents and, where any of the sub-structures have been modified,
Structural scheduling of synthetic cannabinoids
Structural_scheduling_of_synthetic_cannabinoids
Concept in probability theory
Introduction to Schramm–Loewner evolutions (PDF) Pommerenke, Christian (1975), Univalent functions, with a chapter on quadratic differentials by Gerd Jensen, Studia
Schramm–Loewner_evolution
Result of multiplying types in type theory
type product type at the nLab Homotopy Type Theory: Univalent Foundations of Mathematics, The Univalent Foundations Program, Institute for Advanced Study
Product_type
Notion of equality in type theory
208–212. doi:10.1109/LICS.1994.316071. ISBN 0-8186-6310-3. S2CID 19496198. Univalent Foundations Program (12 March 2013). Homotopy Type Theory. Institute for
Identity_type
functions are analytic Schwarzian derivative Analytic capacity Disk algebra Univalent function Ahlfors theory Bieberbach conjecture Borel–Carathéodory theorem
List of complex analysis topics
List_of_complex_analysis_topics
Romanian mathematician (1931–2016)
Gheorghe Călugăreanu, was titled Variational methods in the theory of univalent functions. He continued as faculty at Babeș-Bolyai University, rising
Petru_Mocanu
French-American mathematician
conjecture, posed by Ludwig Bieberbach in 1916, concerns a normalized univalent function f(z)=z+a2z2+a3z3+⋯ on the unit disk and asserts that |an|≤n for
Louis_de_Branges_de_Bourcia
Ring molecules with several ether (–O–) groups
(February 1971). "Stability constants of cyclic polyether complexes with univalent cations". Journal of the American Chemical Society. 93 (3): 600–606. Bibcode:1971JAChS
Crown_ether
Type of musical chord
Heinrich Schenker. He explained that although there is a kinship between all univalent chords rising out of the fifth degree, the dominant ninth chord is not
Diminished_seventh_chord
Chemical element with atomic number 90 (Th)
prepared by heating thorium tetrachloride with limiting KC5H5 used (other univalent metal cyclopentadienyls can also be used). The alkyl and aryl derivatives
Thorium
Negatively charged polyatomic ion containing oxygen
an important factor in these protonation reactions. By contrast, the univalent anions perchlorate and permanganate ions are very difficult to protonate
Oxyanion
German mathematician (1933–2024)
of 1992 original){{cite book}}: CS1 maint: postscript (link) Univalent Functions. Vandenhoeck & Ruprecht. 1975. ISBN 978-3525401330. With Gerd
Christian_Pommerenke
Species of plant
only seven bivalents are formed leaving the other chromosomes as univalents. Univalents are included in egg cells, but not in pollen. Similar processes
Rosa_canina
function type at the nLab Homotopy Type Theory: Univalent Foundations of Mathematics, The Univalent Foundations Program, Institute for Advanced Study
Function_type
Topics referred to by the same term
kernel theorem, a geometric criterion for local uniform convergence of univalent functions Borel–Carathéodory theorem, about the boundedness of a complex
Carathéodory's_theorem
Partial algebra
lemma in semicategories". ncatlab.org. The Univalent Foundations Program (2013). "Homotopy Type Theory: Univalent Foundations of Mathematics". Homotopy Type
Semigroupoid
German mathematician (1902–1993)
mathematician known primarily for his work on complex analysis, specifically univalent functions and conformal mappings, and graph theory. He was the first to
Herbert_Grötzsch
Sperm precursor cell that undergoes meiosis
cleavage furrows are formed in the spermatocyte cells containing four univalent chromosomes. By the end of the anaphase stage, there is one at each pole
Spermatocyte
Italian philosopher
of Mathematics: Univalent Foundations, Set Theory and General Thoughts (Based on the conference on foundations of mathematics: univalent foundations and
Stefania_Centrone
Washington University in St. Louis Geometric studies in the theory of univalent functions Louis Nirenberg New York University Also won 1975 Gerald Enoch
List of Guggenheim Fellowships awarded in 1966
List_of_Guggenheim_Fellowships_awarded_in_1966
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