Implication Details
Claim: If a category is inhabited and is thin, then it has a generator.
Proof: Any object will be a generator for trivial reasons.
This implication has a dual.
Show 22 categories using this implication
- discrete category on two objects
- category of finite sets and bijections
- category of finite sets and surjections
- category of finite abelian groups
- category of finite groups
- partially ordered set of natural numbers
- partially ordered set of extended natural numbers
- partially ordered collection of ordinal numbers
- category of quivers
- category of quivers with finite components
- category of sequences of sets
- category of set functions and commutative squares
- discrete category of sets
- category of pairs of sets
- category of sheaves
- category of large families of vector spaces which are mostly zero
- category of finite Z-sets
- preordered set of integers w.r.t. divisibility
- real interval [0,1]
- walking commutative square
- walking composable pair
- walking span