functor
in category theory, a mapping between categories that preserves their structure (identity morphisms, composition of morphisms)
fibered category
a “sheaf” of categories over a topological space (or, more generally, any category), where instead of equality we have natural equivalences in the definition of the sheaf axioms
group functor
functor from the category of commutative rings to the category of groups
exact functor
functor that preserves short exact sequences
direct image functor
functor between categories of Abelian-group-valued sheaves induced by a map between topological spaces
adjoint functor
relationship that two functors may have
Hom functor
functor mapping hom objects to an underlying category
size functor
mapping used in algebraic topology
faithful functor
functor which is injective when restricted to every hom-set
six operations
formalism in homological algebra
additive functor
concept
smooth functor
functor that sends smoothly parameterized families of vector spaces to smoothly parameterized families of vector spaces
combinatorial species
endofunctor on the category of finite sets and bijections, which can be used to analyse discrete structures in terms of generating functions
amnestic functor
mathematical mapping
morphism of algebraic stacks
type of functor
derived functor
homological construction in category theory
full and faithful functor
functors which are surjective or injective on hom-sets
inverse image functor
functor between categories of Abelian-group-valued sheaves induced by a continuous map between topological spaces; sheafification of the presheaf associating to an open set U the inductive limit of the groups associated to open supersets of U’s image
full functor
Functor surjective on Hom sets
polynomial functor
endofunctor on the category V of finite-dimensional vector spaces
diagram
collection of objects and morphisms in a category