Implication Details
Claim: If a category is left cancellative, then it is Cauchy complete.
Proof: Any idempotent monomorphism must be the identity and therefore splits.
Show 18 categories using this implication
- 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
- delooping of the additive monoid of natural numbers
- delooping of the additive monoid of ordinal numbers
- category of finite sets and injections
- category of fields
- partially ordered set of natural numbers
- partially ordered collection of ordinal numbers
- category of sets and relations
- preordered set of integers w.r.t. divisibility
- forked commutative square
- walking fork
- walking idempotent
- walking parallel pair
- walking span