Implication Details
Claim: If a category has binary powers and is core-thin, then it is thin.
Proof: Let be any object. The swap is an automorphism, hence equal to the identity. It follows that the projections are the same. And this means that every two morphisms are the same.
Show 43 categories using this implication
- category of abelian groups
- category of abelian sheaves
- category of Banach spaces with linear contractions
- category of combinatorial species
- category of commutative algebras
- category of commutative monoids
- category of commutative rings
- category of compact Hausdorff spaces
- category of countable groups
- category of countable sets
- category of finite abelian groups
- category of finite groups
- category of finite ordered sets
- category of finite sets
- category of finite-dimensional vector spaces [countable field]
- category of finite-dimensional vector spaces [finite field]
- category of finite-dimensional vector spaces [uncountable field]
- category of finitely generated abelian groups
- category of free abelian groups
- category of groups
- category of Hausdorff spaces
- category of Jónsson-Tarski algebras
- category of left modules over a division ring
- category of left modules over a ring
- category of M-sets
- category of pairs of sets
- category of pointed sets
- category of set functions and commutative squares
- category of sets
- category of sets and relations
- category of sets with a distinguished subset
- category of sheaves
- category of simplicial sets
- category of torsion abelian groups
- category of vector spaces
- category of Z-functors
- delooping of the additive monoid of natural numbers
- delooping of the additive monoid of ordinal numbers
- simplex category
- walking coreflexive pair
- walking idempotent
- walking parallel pair
- walking splitting