- function. The two
presheaf axioms are
immediately checked,
thereby giving an
example of a
presheaf. This can be
extended to a
presheaf of
holomorphic functions...
- In
category theory, a
branch of mathematics, a
presheaf on a
category C {\displaystyle C} is a
functor F : C o p → S e t {\displaystyle F\colon C^{\mathrm...
- mathematics, more
specifically in
homotopy theory, a
simplicial presheaf is a
presheaf on a site (e.g., the
category of
topological spaces)
taking values...
- a
presheaf on X {\displaystyle X} is a
contravariant functor from O ( X ) {\displaystyle O(X)} to the
category of sets, and a
sheaf is a
presheaf that...
- In
algebraic geometry, a
presheaf with
transfers is, roughly, a
presheaf that, like
cohomology theory,
comes with pushforwards, “transfer” maps. Precisely...
-
category of
elements of a
presheaf is a
category ****ociated to that
presheaf whose objects are the
elements of sets in the
presheaf. It and its generalization...
-
topological space X {\displaystyle X} must satisfy,
given that it is a
presheaf,
which is by
definition a
contravariant functor F : O ( X ) → C {\displaystyle...
- theory, one can
consider a
presheaf on an ∞-category C. From the
point of view of
higher category theory, such a
presheaf should not be set-valued but...
-
every presheaf of sets is a
colimit of
representable presheaves in a
canonical way. For example, by definition, a
simplicial set is a
presheaf on the...
- {A}}} or A X {\displaystyle A_{X}} . The
constant presheaf with
value A {\displaystyle A} is the
presheaf that ****igns to each open
subset of X {\displaystyle...
