Implication details
Claim: If a category is regular-subobject-trivial, then it is retract-trivial.
Proof: This follows from the fact that every split monomorphism is a regular monomorphism.
This implication has a dual.
Show 23 categories using this implication
- category of finite sets and bijections
- delooping of the bicyclic monoid
- delooping of the double bicyclic monoid
- delooping of a group
- delooping of an infinite countable group
- delooping of a non-trivial finite group
- delooping of an infinite uncountable group
- simplex category
- category of finite sets and surjections
- category of finite ordered sets
- category of finite sets of odd cardinality
- category of finite sets of cardinality a power of 3
- category of measurable spaces
- category of partially ordered sets without isolated points
- category of sets and bijections
- category of countably infinite sets
- category of large families of sets and bijections
- category of non-empty sets
- category of uniform spaces
- forked commutative square
- walking coreflexive pair
- walking idempotent
- walking splitting