-
notion of a
colimit generalizes constructions such as
disjoint unions,
direct sums, coproducts,
pushouts and
direct limits.
Limits and
colimits, like the...
-
Cohomology of
categories Spectral sequence of
homotopy colimits Dugger, Daniel. "A
Primer on
Homotopy Colimits" (PDF).
Archived (PDF) from the
original on 3 Dec...
- 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...
-
category C ^ {\displaystyle {\widehat {C}}}
admits small limits and
small colimits. Explicitly, if f : I → C ^ {\displaystyle f:I\to {\widehat {C}}} is a...
- is
cocontinuous (i.e.
commutes with
colimits).
Since many
common constructions in
mathematics are
limits or
colimits, this
provides a
wealth of information...
-
terminal objects to
terminal objects, and any
functor which preserves colimits will take
initial objects to
initial objects. For example, the initial...
- a
general theorem of
category theory, they have all
finite limits and
colimits. That is, pre-abelian
categories are
finitely complete. The
existence of...
-
category C are: C has a
small set of generators, and
admits all
small colimits. Furthermore,
fiber products distribute over coproducts. That is, given...
-
filtered colimits, has an
extension F ~ : Ind ( C ) → D , {\displaystyle {\tilde {F}}:\operatorname {Ind} (C)\to D,} that
preserves filtered colimits. This...
- \operatorname {Hom} (X,-)}
preserves all κ {\displaystyle \kappa } -directed
colimits in C {\displaystyle C} . It is
clear that
every κ {\displaystyle \kappa...
