Implication Details
Assumptions: locally cartesian closed, terminal object
Conclusions: cartesian closed
Proof: The slice over the terminal object is the category itself.
Show 38 categories using this implication
- category of abelian groups
- category of abelian sheaves
- category of algebras
- category of commutative algebras
- category of commutative rings
- category of compact Hausdorff spaces
- category of countable groups
- category of countable sets
- category of filtered vector spaces
- category of finite abelian groups
- category of finite groups
- 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 left modules over a division ring
- category of left modules over a ring
- category of locally ringed spaces
- category of metric spaces with continuous maps
- category of metric spaces with non-expansive maps
- category of metric spaces with ∞ allowed
- category of pointed sets
- category of pseudo-metric spaces with non-expansive maps
- category of rings
- category of schemes
- category of semigroups
- category of sets with a distinguished subset
- category of torsion abelian groups
- category of torsion-free abelian groups
- category of vector spaces
- category of Z-functors
- poset [0,1]
- poset of extended natural numbers
- proset of integers w.r.t. divisibility
- walking commutative square
- walking composable pair
- walking morphism