Implication details
Claim: If a category is locally cocartesian coclosed, then it has pushouts.
Proof: This follows from the dual implication.
This implication has a dual.
Show 21 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 an irreflexive binary relation
- category of sets equipped with a symmetric irreflexive binary relation
- category of coproducts of Euclidean spaces
- category of finite groups
- category of finite sets of even cardinality
- category of fields
- category of free abelian groups
- category of finitely generated free modules over Z x Z
- category of smooth manifolds
- partially ordered set of natural numbers
- partially ordered collection of ordinal numbers
- category of partially ordered sets without isolated points
- category of sets and relations
- category of schemes
- category of sets with finite-to-one maps
- walking commutative square
- walking idempotent
- walking parallel pair
- walking span