Implication Details
Claim: If a category is a groupoid, then it has directed colimits and is epi-regular and has pushouts and is right cancellative and is self-dual and is well-copowered.
Proof: This follows from the dual implication.
This implication has a dual.
Show 13 categories using this implication
- empty category
- trivial category
- discrete category on two objects
- category of finite sets and bijections
- delooping of a group
- delooping of an infinite countable group
- delooping of a non-trivial finite group
- delooping of an infinite uncountable group
- category of sets and bijections
- discrete category of sets
- category of large families of sets and bijections
- indiscrete category of sets
- walking isomorphism