Implication Details
Claim: If a category is one-sorted finitary algebraic, then it is well-copowered.
Proof: See MSE/486607. Alternatively, one may combine the facts that one-sorted finitary algebraic categories are locally (finitely) presentable and that locally presentable categories are well-copowered, both of which are saved in the database. But we include the direct proof here as well, since it makes it easier to deduce the property for one-sorted finitary algebraic categories appearing in practice.
Show 23 categories using this implication
- trivial category
- category of abelian groups
- category of algebras
- category of commutative algebras
- category of commutative monoids
- category of commutative rings
- category of groups
- category of Jónsson-Tarski algebras
- category of M-sets
- category of monoids
- partially ordered collection of ordinal numbers
- category of left modules over a ring
- category of left modules over a division ring
- category of left modules over a non-semisimple ring
- category of rings
- category of rngs
- category of semigroups
- category of sets
- category of pointed sets
- category of vector spaces
- category of Z-functors
- walking isomorphism
- walking morphism