Implication details
Claim: If a category is regular-quotient-trivial, then it is retract-trivial.
Proof: This follows from the dual implication.
This implication has a dual.
Show 23 categories using this implication
- delooping of the bicyclic monoid
- delooping of the double bicyclic monoid
- delooping of the additive monoid of natural numbers
- delooping of the additive monoid of ordinal numbers
- category of sets equipped with an irreflexive binary relation
- category of sets equipped with a symmetric irreflexive binary relation
- category of coproducts of Euclidean spaces
- category of finite sets and injections
- category of finite ordered sets
- category of finite sets
- category of finite sets of even cardinality
- category of fields
- category of fields of characteristic zero
- category of smooth manifolds
- category of measurable spaces
- category of sets with a distinguished subset
- category of partially ordered sets without isolated points
- category of quivers with finite components
- category of rngs
- category of countably infinite sets
- category of sets with finite-to-one maps
- category of uniform spaces
- walking splitting