Implication Details
Claim: If a category has an initial object and has wide pushouts, then it is cocomplete.
Proof: This follows from the dual implication.
This implication has a dual.
Show 14 categories using this implication
- category of finitely generated abelian groups
- category of sets equipped with an irreflexive binary relation
- category of sets equipped with a symmetric irreflexive binary relation
- category of finite abelian groups
- category of finite groups
- category of fields of characteristic zero
- partially ordered set of natural numbers
- category of finitely generated projective modules over the ring of dual numbers
- category of quivers with finite components
- category of sets with finite-to-one maps
- category of finite Z-sets
- forked commutative square
- walking fork
- walking splitting