Implication details
Claim: If a category is retract-trivial, then it has effective cocongruences.
Proof: This follows from the dual implication.
This implication has a dual.
Show 22 categories using this implication
- category of algebras
- category of commutative monoids
- category of small categories
- category of finite sets and surjections
- category of fields
- category of fields of characteristic zero
- category of locally ringed spaces
- category of measurable spaces
- category of extended metric spaces
- category of monoids
- category of pseudo-metric spaces with non-expansive maps
- category of partially ordered sets
- category of partially ordered sets without isolated points
- category of preordered sets
- category of rings
- category of rngs
- category of semigroups
- category of sets and bijections
- category of countably infinite sets
- category of large families of sets and bijections
- category of topological spaces
- category of uniform spaces