-
notion of a
colimit generalizes constructions such as
disjoint unions,
direct sums, coproducts,
pushouts and
direct limits.
Limits and
colimits, like the...
- 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...
-
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 U : Top → Set
uniquely lifts both
limits and
colimits and
preserves them as...
-
Cohomology of
categories Spectral sequence of
homotopy colimits Dugger, Daniel. "A
Primer on
Homotopy Colimits" (PDF).
Archived (PDF) from the
original on 3 Dec...
- {\displaystyle C} has a
small set of generators, and
admits all
small colimits. Furthermore,
fiber products distribute over coproducts; that is, given...
- is
cocontinuous (i.e.
commutes with
colimits).
Since many
common constructions in
mathematics are
limits or
colimits, this
provides a
wealth of information...
- \operatorname {Hom} (X,-)}
preserves all κ {\displaystyle \kappa } -directed
colimits in C {\displaystyle C} . It is
clear that
every κ {\displaystyle \kappa...
-
colimits of
category theory. The
terminology is
somewhat confusing:
inverse limits are a
class of limits,
while direct limits are a
class of
colimits...
- 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...
