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polynomial functor is an endofunctor on the category V {\displaystyle {\mathcal {V}}} of finite-dimensional vector spaces that depends polynomially on...

In type theory, a polynomial functor (or container functor) is a kind of endofunctor of a category of types that is intimately related to the concept of...

In mathematics, specifically category theory, a functor is a mapping between categories. Functors were first considered in algebraic topology, where algebraic...

relationship that two functors may exhibit, intuitively corresponding to a weak form of equivalence between two related categories. Two functors that stand in...

approximating functors are required to be "k-excisive" – such functors are called polynomial functors by analogy with Taylor polynomials – which is a simplifying...

of algebra, a polynomial ring or polynomial algebra is a ring (which is also a commutative algebra) formed from the set of polynomials in one or more...

geometry, a functor represented by a scheme X is a set-valued contravariant functor on the category of schemes such that the value of the functor at each...

category theory, a representable functor is a certain functor from an arbitrary category into the category of sets. Such functors give representations of an...

output type) is also indexed by shape. Container (abstract data type) Polynomial functor (type theory) Michael Abbott; Thorsten Altenkirch; Neil Ghani (2005)...

{\displaystyle C_{2}} , and if F : C 1 → C 2 {\displaystyle F:C_{1}\to C_{2}} is a functor mapping X 1 {\displaystyle X_{1}} to X 2 {\displaystyle X_{2}} , then F...

Each W-type is isomorphic to the initial algebra of a so-called polynomial functor. Let 0, 1, 2, etc. be finite types with inhabitants 11 : 1, 12, 22:2...

directed graph. polynomial A functor from the category of finite-dimensional vector spaces to itself is called a polynomial functor if, for each pair...

conjecture, which concerns the sufficiency of a polynomial mapping to be invertible. Polynomial functor Claudio Procesi (2007) Lie Groups: an approach...

analogue of a polynomial ring since its elements may be described as "polynomials" with non-commuting variables. Likewise, the polynomial ring may be regarded...

In mathematics, the Ext functors are the derived functors of the Hom functor. Along with the Tor functor, Ext is one of the core concepts of homological...

k-Schur functions Grothendieck polynomials (K-theoretical analogue of Schur polynomials) LLT polynomials Schur functor Littlewood–Richardson rule, where...

direct image functor, taking sheaves and their morphisms on the domain to sheaves and morphisms on the codomain, and an inverse image functor operating in...

homogeneous symmetric polynomials are a specific kind of symmetric polynomials. Every symmetric polynomial can be expressed as a polynomial expression in complete...

mathematics, the Tor functors are the derived functors of the tensor product of modules over a ring. Along with the Ext functor, Tor is one of the central...

especially in the field of representation theory, Schur functors (named after Issai Schur) are certain functors from the category of modules over a fixed commutative...