Implication Details
Claim: If a category has disjoint products and has a generating collection, then it has a generator.
Proof: This follows from the dual implication.
This implication has a dual.
Show 16 categories using this implication
- empty category
- category of finite sets and bijections
- category of finite sets and surjections
- category of finite abelian groups
- category of finite groups
- category of fields
- category of fields of characteristic zero
- category of quivers
- category of quivers with finite components
- category of sequences of sets
- category of set functions and commutative squares
- category of pairs of sets
- category of empty-or-finite pairs of sets
- category of sheaves
- category of combinatorial species
- category of finite Z-sets