- open
subsets gives rise to the
concept of
presheaves.
Roughly speaking,
sheaves are then
those presheaves,
where local data can be
glued to
global data...
- space. A
morphism of
presheaves is
defined to be a
natural transformation of functors. This
makes the
collection of all
presheaves on C {\displaystyle...
- In
category theory, a
branch of mathematics, a
limit or a
colimit of
presheaves on a
category C is a
limit or
colimit in the
functor category C ^ = F c...
-
concretely a Kan complex, as a space.
Given that, we take the
category of "∞-
presheaves" on C to be C ^ = Hom _ ( C o p , Kan ) {\displaystyle {\widehat {C}}={\underline...
- }}} (the
presheaves over C) of
retracts of
representable functors. The
category of
presheaves on C is
equivalent to the
category of
presheaves on Split(C)...
- of
simplicial presheaves on a site
admits several different model structures. Some of them are
obtained by
viewing simplicial presheaves as
functors S...
- "category of
right modules over C {\displaystyle C} ". The
category of
presheaves on a
topological space X {\displaystyle X} is a
functor category: we turn...
- Set, the
category of sets and functions, D is
called a
presheaf on C.
Presheaves (over a
topological space) If X is a
topological space, then the open...
- is true.
Given a
small category C {\displaystyle C} , the
category of
presheaves S e t C o p {\displaystyle \mathrm {Set} ^{C^{op}}} (i.e. the functor...
-
category of G {\displaystyle G} -sets. We
construct this as the
category of
presheaves on the
category with one object, but now the set of
morphisms is given...
