Implication details
Claim: If a category is inverse, then it has sequential colimits.
Proof: This follows from the dual implication.
This implication has a dual.
Show 20 categories using this implication
- empty category
- trivial category
- discrete category on two objects
- delooping of the additive monoid of ordinal numbers
- simplex category
- category of finite sets and injections
- category of finite groups
- category of finite ordered sets
- category of free abelian groups
- category of smooth manifolds
- category of metric spaces with continuous maps
- partially ordered set of natural numbers
- category of quivers with finite components
- category of schemes
- discrete category of sets
- forked commutative square
- walking fork
- walking idempotent
- walking parallel pair
- walking span