Implication details
Claim: If a category has cokernels and is inhabited, then it has an initial object.
Proof: This follows from the dual implication.
This implication has a dual.
Show 19 categories using this implication
- trivial category
- discrete category on two objects
- category of large families of abelian groups
- category of finitely generated abelian groups
- category of finite sets and bijections
- category of filtered vector spaces
- category of finite-dimensional vector spaces
- category of finite-dimensional vector spaces [countable field]
- category of finite-dimensional vector spaces [finite field]
- category of finite-dimensional vector spaces [uncountable field]
- category of connected sequences of sets
- category of large families of sets which are mostly singletons
- indiscrete category of sets
- category of non-empty sets
- category of abelian sheaves
- category of long transfinite sequences of abelian groups
- category of vector spaces
- category of large vector spaces over a large field with a small basis
- walking isomorphism