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 56 categories using this implication
- empty category
- discrete category on two objects
- category of finitely generated abelian groups
- delooping of the bicyclic monoid
- delooping of the double bicyclic monoid
- delooping of the additive monoid of natural 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
- category of small categories
- simplex category
- category of coproducts of Euclidean spaces
- 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 finitely generated groups
- category of Hausdorff spaces
- category of locally ringed spaces
- category of measurable spaces
- category of metric spaces with non-expansive maps
- category of metric spaces with continuous maps
- category of extended metric spaces
- 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 quivers with finite components
- category of schemes
- category of connected sequences of sets
- category of countable sets
- category of countably infinite 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 empty-or-finite pairs of sets
- category of combinatorial species
- category of topological spaces
- category of Z-functors
- category of finite Z-sets
- cocompletion of a discrete–pair join
- category of ω-sets
- walking idempotent
- walking span