- Dually, a
cocomplete category is one in
which all
small colimits exist. A
bicomplete category is a
category which is both
complete and
cocomplete. The existence...
- a
small posetal finitely cocomplete cartesian closed category, and a
Boolean algebra as a
small posetal finitely cocomplete *-autonomous category. Conversely...
-
tensor algebra is a free algebra, the
corresponding coalgebra is
termed cocomplete co-free. With the
usual product this is not a bialgebra. It can be turned...
-
category C
where every diagram from a
small category to C has a limit; it is
cocomplete if
every such
functor has a
colimit Completeness (order theory), a notion...
- a
cosmos is a
symmetric closed monoidal category that is
complete and
cocomplete.
Enriched category theory is
often considered over a cosmos.
cosmos at...
-
properties of D {\displaystyle D} : if D {\displaystyle D} is
complete (or
cocomplete), then so is D C {\displaystyle D^{C}} ; if D {\displaystyle D} is an...
-
subobjects are classified.
Quasitoposes are also
required to be
finitely cocomplete and
locally cartesian closed. A
solid quasitopos is one for
which 0 is...
-
family (Ai) of
objects of A, the
coproduct *Ai
exists in A (i.e. A is
cocomplete). AB4) A
satisfies AB3), and the
coproduct of a
family of monomorphisms...
-
football club
based in
Mbabane Cosmos (category theory), a
complete and
cocomplete symmetric closed monoidal category in
mathematics Cosmos (plant), a genus...
- F:\mathbf {A} \to \mathbf {B} } are two functors. If A is
small and C is
cocomplete, then
there exists a left Kan
extension Lan F X {\displaystyle \operatorname...
