Implication details
Claim: If a category is an elementary cotopos, then it has disjoint finite products and has effective cocongruences and is finitely complete and is locally cocartesian coclosed.
Proof: This follows from the dual implication.
This implication has a dual.
Show 42 categories using this implication
- category of algebras
- category of finite sets and bijections
- category of commutative monoids
- category of small categories
- simplex category
- 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 finite-dimensional vector spaces
- 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 Hausdorff spaces
- category of locally ringed spaces
- category of measurable spaces
- category of metric spaces with non-expansive maps
- category of extended metric spaces
- category of monoids
- partially ordered set of extended natural numbers
- partially ordered collection of ordinal numbers
- category of pseudo-metric spaces with non-expansive maps
- category of partially ordered sets
- category of partially ordered sets without isolated points
- category of preordered sets
- category of finitely generated projective modules over the ring of dual numbers
- category of rings
- category of rngs
- category of semigroups
- category of connected sequences of sets
- category of countably infinite sets
- discrete category of sets
- category of large families of sets which are mostly singletons
- category of topological spaces
- category of pointed topological spaces
- category of uniform spaces
- category of large families of vector spaces which are mostly zero
- forked commutative square
- walking coreflexive pair
- walking morphism
- walking parallel pair