Implication Details
Claim: If a category is Grothendieck abelian, then it has a cogenerator.
Proof: See Kashiwara-Schapira, Thm. 9.6.3.
Show 20 categories using this implication
- category of abelian groups
- category of finitely generated abelian groups
- category of commutative monoids
- category of cochain complexes of abelian groups
- category of finite sets and injections
- category of groups
- category of countable groups
- category of Hausdorff spaces
- category of monoids
- 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 rngs
- category of semigroups
- category of sequences of abelian groups
- category of sets with finite-to-one maps
- category of abelian sheaves
- category of torsion abelian groups
- category of graded abelian groups
- category of graded modules over a graded ring