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.
This implication has a dual.
Show 27 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 coproducts of Euclidean spaces
- category of finite sets and injections
- category of finite sets of even cardinality
- 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 finitely generated free modules over Z x Z
- partially ordered set of natural numbers
- partially ordered collection of ordinal numbers
- category of partially ordered sets without isolated points
- category of sets and relations
- category of sets and bijections
- category of large families of sets and bijections
- preordered set of integers w.r.t. divisibility
- forked commutative square
- walking fork
- walking idempotent
- walking parallel pair
- walking span