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In category theory, a branch of mathematics, a subfunctor is a special type of functor that is an analogue of a subset. Let C be a category, and let F...

/ F p {\displaystyle {\textbf {Sch}}/\mathbb {F} _{p}} , there is the subfunctor α p {\displaystyle \alpha _{p}} where α p ( X ) = { x ∈ O ( X ) : x p...

the notion of a sieve. If c is any given object in C, a sieve on c is a subfunctor of the functor Hom(−, c); (this is the Yoneda embedding applied to c)...

let UN be the functor C → Set determined by UN(c) = (U(c))N. Then a subfunctor of UN is called an N-ary predicate and a natural transformation UN → U...

of ordinals cannot be fully embedded in the category of graphs. Every subfunctor of an accessible functor is accessible. (In a definable classes setting)...

\prod X(R_{f_{i}f_{j}})} Also, there must exist open affine subfunctors U i = Spec ( A i ) = Hom CAlg ( A i , − ) {\displaystyle...

functor which has a natural stratification into a disjoint union of subfunctors, each of which is represented by a projective S {\displaystyle S} -scheme...

In mathematics, a preradical is a subfunctor of the identity functor in the category of left modules over a ring with identity. The class of all preradicals...

→ S e t {\displaystyle S\colon C^{\rm {op}}\to {\rm {Set}}} on c is a subfunctor of Hom(−, c), i.e., for all objects c′ of C, S(c′) ⊆ Hom(c′, c), and for...