Implication Details
Assumptions: equalizers, right cancellative
Conclusions: thin
Proof: If are two parallel morphisms, then their equalizer is a regular monomorphism, but also an epimorphism by assumption, so it must be an isomorphism. But this means that .
Show 30 categories using this implication
- category of abelian sheaves
- category of combinatorial species
- category of countable groups
- category of countable sets
- category of finite abelian groups
- category of finite groups
- category of finite sets
- category of finite sets and bijections
- category of finite sets and injections
- category of finite sets and surjections
- category of finite-dimensional vector spaces [countable field]
- category of finite-dimensional vector spaces [finite field]
- category of finite-dimensional vector spaces [uncountable field]
- category of finitely generated abelian groups
- category of free abelian groups
- category of Jónsson-Tarski algebras
- category of M-sets
- category of pairs of sets
- category of schemes
- category of sets
- category of sets with finite-to-one maps
- category of sheaves
- category of simplicial sets
- 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
- walking fork
- walking parallel pair
- walking splitting