Definition of Cocomplete. Meaning of Cocomplete. Synonyms of Cocomplete

- 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...
- 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...
- 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...
- subobjects are classified. Quasitoposes are also required to be finitely cocomplete and locally cartesian closed. A solid quasitopos is one for which 0 is...
- a cosmos is a symmetric closed monoidal category that is complete and cocomplete. Enriched category theory is often considered over a cosmos. cosmos at...
- a small posetal finitely cocomplete cartesian closed category, and a Boolean algebra as a small posetal finitely cocomplete *-autonomous category. Conversely...
- by the direct sum; since Ab has cokernels, it follows that Ab is also cocomplete. We have a forgetful functor Ab → Set which ****igns to each abelian group...
- 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...
- that there is a natural equivalence between geometric morphisms from a cocomplete topos E to T and the category of models for the structure in E. The classifying...
- and unique lifting of limits). The category Top is both complete and cocomplete, which means that all small limits and colimits exist in Top. In fact...