Implication Details
Claim: If a category is left cancellative, then it has coreflexive equalizers and has effective cocongruences and has effective congruences and has reflexive coequalizers.
Proof: Any parallel pair of morphisms with a common section (or retraction) must be a pair of equal isomorphisms. In particular, they are the kernel pair of , and the cokernel pair of .
Show 43 categories using this implication
- category of algebras
- category of fields
- category of finite sets and bijections
- category of finite sets and injections
- category of locally ringed spaces
- category of measurable spaces
- category of metric spaces with continuous maps
- category of metric spaces with non-expansive maps
- category of metric spaces with ∞ allowed
- category of monoids
- category of non-empty sets
- category of partially ordered sets
- category of pointed topological spaces
- category of preordered sets
- category of pseudo-metric spaces with non-expansive maps
- category of rings
- category of rngs
- category of schemes
- category of semigroups
- category of sets and relations
- category of sets with finite-to-one maps
- category of small categories
- category of smooth manifolds
- category of topological spaces
- 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
- discrete category on two objects
- empty category
- partially ordered collection of ordinal numbers
- partially ordered set of natural numbers
- preordered set of integers w.r.t. divisibility
- real interval [0,1]
- simplex category
- trivial category
- walking coreflexive pair
- walking fork
- walking idempotent
- walking isomorphism
- walking parallel pair
- walking span