Implication Details
Assumptions: left cancellative
Conclusions: Cauchy complete
Proof: Any idempotent monomorphism must be the identity and therefore splits.
Show 16 categories using this implication
- category of fields
- category of finite sets and bijections
- category of finite sets and injections
- category of sets and relations
- delooping of a non-trivial finite group
- delooping of an infinite countable group
- delooping of an infinite uncountable group
- delooping of the additive monoid of natural numbers
- delooping of the additive monoid of ordinal numbers
- poset of natural numbers
- poset of ordinal numbers
- proset of integers w.r.t. divisibility
- walking fork
- walking idempotent
- walking parallel pair
- walking span