Implication details
Claim: If a category is cartesian closed and has a strict terminal object, then it is thin.
Proof: If a morphism exists, we get a morphism , which forces to be a terminal object by assumption. But then any two morphisms are equal, so that any two morphisms are equal.
This implication has a dual.
Show 26 categories using this implication
- category of algebras
- category of sets equipped with a binary relation
- category of sets equipped with a reflexive binary relation
- category of sets equipped with a symmetric binary relation
- category of sets equipped with a symmetric reflexive binary relation
- category of commutative algebras
- category of commutative rings
- category of small categories
- category of F(I)-sets
- category of Jónsson-Tarski algebras
- category of M-sets
- category of sets with a distinguished subset
- category of partially ordered sets
- category of preordered sets
- category of quivers
- category of rings
- 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 Z-sets
- category of ω-sets
- category of simplicial sets