-
notion of a
colimit generalizes constructions such as
disjoint unions,
direct sums, coproducts,
pushouts and
direct limits.
Limits and
colimits, like the...
-
terminal objects to
terminal objects, and any
functor which preserves colimits will take
initial objects to
initial objects. For example, the initial...
- all
small limits and
colimits exist in Top. In fact, the
forgetful functor UĀ : Top ā Set
uniquely lifts both
limits and
colimits and
preserves them as...
- {\displaystyle C} has a
small set of generators, and
admits all
small colimits. Furthermore,
fiber products distribute over coproducts; that is, given...
-
Cohomology of
categories Spectral sequence of
homotopy colimits Dugger, Daniel. "A
Primer on
Homotopy Colimits" (PDF).
Archived (PDF) from the
original on 3 Dec...
- and form the
colimit of this functor. One can show that a
category has all
directed limits if and only if it has all
filtered colimits, and a functor...
- is
cocontinuous (i.e.
commutes with
colimits).
Since many
common constructions in
mathematics are
limits or
colimits, this
provides a
wealth of information...
-
category limit can be
developed and
dualized to
yield the
notion of a
colimit. It is a
natural question to ask:
under which conditions can two categories...
-
category C ^ {\displaystyle {\widehat {C}}}
admits small limits and
small colimits. Explicitly, if f : I ā C ^ {\displaystyle f:I\to {\widehat {C}}} is a...
- w:j\to k} such that w u = w v {\displaystyle wu=wv} . A
filtered colimit is a
colimit of a
functor F : J ā C {\displaystyle F:J\to C}
where J {\displaystyle...
