Implication Details
Claim: A category is quotient-trivial if and only if it is epi-regular and is regular-quotient-trivial.
Proof: This follows from the dual implication.
Show 40 categories using this implication
- category of abelian sheaves
- category of combinatorial species
- category of compact Hausdorff spaces
- category of countable groups
- category of countable sets
- category of finite abelian groups
- category of finite groups
- category of finite ordered sets
- 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 metric spaces with non-expansive maps
- category of pairs of sets
- category of pointed sets
- category of pseudo-metric spaces with non-expansive maps
- category of set functions and commutative squares
- category of sheaves
- 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
- partially ordered collection of ordinal numbers
- partially ordered set of extended natural numbers
- partially ordered set of natural numbers
- preordered set of integers w.r.t. divisibility
- real interval [0,1]
- walking commutative square
- walking composable pair
- walking fork
- walking idempotent
- walking morphism
- walking parallel pair
- walking span
- walking splitting