-
notion of a
colimit generalizes constructions such as
disjoint unions,
direct sums, coproducts,
pushouts and
direct limits.
Limits and
colimits, like the...
-
homotopy limit and
colimitpg 52 are
variants of the
notions of
limit and
colimit extended to the
homotopy category Ho ( Top ) {\displaystyle {\text{Ho}}({\textbf...
- 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 t ( C op ,...
- w:j\to k} such that w u = w v {\displaystyle wu=wv} . A
filtered colimit is a
colimit of a
functor F : J → C {\displaystyle F:J\to C}
where J {\displaystyle...
-
sends each
diagram to its limit. Dually, the
colimit of
diagram D is a
universal cone from D. If the
colimit exists for all
diagrams of type J one has a...
-
system of homomorphisms.
Direct limits are a
special case of the
concept of
colimit in
category theory.
Direct limits are dual to
inverse limits,
which are...
- : D → Set {\displaystyle G:D\to {\textbf {Set}}} , the
colimit of G is the same as the
colimit of G ∘ F {\displaystyle G\circ F} . Note that an object...
-
category to C has a limit; it is
cocomplete if
every such
functor has a
colimit Completeness (order theory), a
notion that
generally refers to the existence...
- and
small colimits. See
limit and
colimit of
presheaves for
further discussion. The
density theorem states that
every presheaf is a
colimit of representable...
-
characterised as a
terminal object in the
category of
cones to F. Likewise, a
colimit of F may be
characterised as an
initial object in the
category of co-cones...
