Implication details
Claim: If a category has finite copowers, then it has binary copowers and has an initial object.
Proof: This follows from the dual implication.
This implication has a dual.
Show 23 categories using this implication
- empty category
- discrete category on two objects
- category of finite sets and bijections
- delooping of the additive monoid of natural numbers
- delooping of the additive monoid of ordinal numbers
- simplex category
- category of finite sets and injections
- category of finite sets and surjections
- category of finite groups
- category of finite ordered sets
- category of finite sets of odd cardinality
- category of finite sets of cardinality a power of 3
- category of fields
- category of fields of characteristic zero
- category of metric spaces with non-expansive maps
- category of pseudo-metric spaces with non-expansive maps
- category of connected sequences of sets
- category of sets and bijections
- discrete category of sets
- category of large families of sets and bijections
- category of large families of sets which are mostly singletons
- category of non-empty sets
- category of empty-or-finite pairs of sets