Implication Details
Claim: If a category is locally cartesian closed, then it has pullbacks.
Proof: Pullbacks are binary products in slice categories.
This implication has a dual.
Show 48 categories using this implication
- delooping of the additive monoid of natural numbers
- delooping of the additive monoid of ordinal numbers
- category of sets equipped with a binary relation
- category of sets equipped with an irreflexive 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 irreflexive binary relation
- category of sets equipped with a symmetric reflexive binary relation
- simplex category
- category of coproducts of Euclidean spaces
- category of finite sets and injections
- category of finite sets and surjections
- category of finite ordered sets
- category of finite sets
- category of finite sets of odd cardinality
- category of finite sets of cardinality a power of 3
- category of finitely generated free modules over Z x Z
- category of Jónsson-Tarski algebras
- category of M-sets
- category of smooth manifolds
- category of sets with a distinguished subset
- partially ordered set of natural numbers
- partially ordered set of extended natural numbers
- partially ordered collection of ordinal numbers
- category of partially ordered sets without isolated points
- category of quivers
- category of sets and relations
- category of sequences of sets
- category of sets
- category of set functions and commutative squares
- category of large families of sets which are mostly empty
- category of large families of sets which are mostly singletons
- category of sets with finite-to-one maps
- category of non-empty sets
- category of pairs of sets
- category of sheaves
- category of combinatorial species
- category of finite Z-sets
- category of Z-sets
- cocompletion of a discrete–pair join
- forked commutative square
- category of simplicial sets
- walking commutative square
- walking coreflexive pair
- walking fork
- walking idempotent
- walking parallel pair
- walking span