Implication Details
Claim: If a category is locally cartesian closed and has a terminal object, then it is cartesian closed.
Proof: The slice over the terminal object is the category itself.
This implication has a dual.
Show 30 categories using this implication
- 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 compact Hausdorff spaces
- category of free abelian groups
- category of countable groups
- category of locally ringed spaces
- category of metric spaces with non-expansive maps
- category of metric spaces with continuous maps
- category of metric spaces with ∞ allowed
- category of sets with a distinguished subset
- partially ordered set of extended natural numbers
- category of pseudo-metric spaces with non-expansive maps
- category of quivers with finite components
- category of schemes
- category of semigroups
- category of connected sequences of sets
- category of countable sets
- category of large families of sets which are mostly singletons
- category of empty-or-finite pairs of sets
- category of uniform spaces
- category of countable-dimensional vector spaces
- category of large vector spaces over a large field with a small basis
- category of Z-functors
- preordered set of integers w.r.t. divisibility
- real interval [0,1]
- walking commutative square
- walking composable pair
- walking morphism