Implication Details
Claim: If a category is countably extensive, then it has countable coproducts.
Proof: This holds by definition.
This implication has a dual.
Show 63 categories using this implication
- empty category
- trivial category
- discrete category on two objects
- category of finitely generated abelian groups
- category of finite sets and bijections
- delooping of a group
- delooping of an infinite countable group
- delooping of a non-trivial finite group
- delooping of an infinite uncountable group
- delooping of the additive monoid of natural numbers
- category of sets with a binary relation
- category of small categories
- simplex category
- category of directed graphs
- category of coproducts of Euclidean spaces
- category of finite sets and injections
- category of finite sets and surjections
- category of finite abelian groups
- category of finite groups
- 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 [countable field]
- category of finite-dimensional vector spaces [finite field]
- category of finitely generated free abelian groups
- category of finitely generated free modules over Z x Z
- category of Hausdorff spaces
- category of Jónsson-Tarski algebras
- category of locally ringed spaces
- category of M-sets
- category of measurable spaces
- category of metric spaces with non-expansive maps
- category of metric spaces with continuous maps
- category of metric spaces with ∞ allowed
- partially ordered set of natural 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 schemes
- category of sets
- category of set functions and commutative squares
- category of countable sets
- discrete category of sets
- 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 pairs of sets
- category of sheaves
- category of combinatorial species
- category of topological spaces
- category of Z-functors
- cocompletion of a discrete–pair join
- forked commutative square
- category of simplicial sets
- walking coreflexive pair
- walking fork
- walking idempotent
- walking isomorphism
- walking parallel pair
- walking span
- walking splitting