Implication Details
Claim: If a category is essentially finite and has finite powers, then it is thin.
Proof: Adjust the proof of Mac Lane, V.2, Prop. 3.
This implication has a dual.
Show 38 categories using this implication
- delooping of a non-trivial finite group
- category of commutative monoids
- category of coproducts of Euclidean spaces
- category of F(I)-sets
- category of finite abelian groups
- category of finite groups
- category of finite sets
- category of finite sets of odd cardinality
- category of finite sets of cardinality a power of 3
- category of finite-dimensional vector spaces
- category of finite-dimensional vector spaces [finite field]
- category of countable groups
- category of Jónsson-Tarski algebras
- category of M-sets
- category of quivers
- category of quivers with finite components
- category of sets and relations
- category of schemes
- category of sequences of sets
- category of sets
- category of set functions and commutative squares
- category of large families of sets
- category of non-empty sets
- category of pairs of sets
- category of sheaves
- category of abelian sheaves
- category of torsion abelian groups
- category of long transfinite sequences of abelian groups
- category of large families of vector spaces which are mostly zero
- category of large vector spaces over a large field with a small basis
- category of finite Z-sets
- category of Z-sets
- forked commutative square
- category of simplicial sets
- walking coreflexive pair
- walking idempotent
- walking parallel pair
- walking splitting