Implication Details
Assumptions: extensive
Conclusions: disjoint finite coproducts, strict initial object
Proof: These are Prop. 2.6 and 2.8 in Introduction to extensive and distributive categories.
Show 48 categories using this implication
- category of abelian groups
- category of abelian sheaves
- category of combinatorial species
- category of compact Hausdorff spaces
- category of countable sets
- category of filtered vector spaces
- category of finite abelian groups
- category of finite sets
- 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 finitely generated abelian groups
- category of free abelian groups
- category of Hausdorff spaces
- category of Jónsson-Tarski algebras
- category of left modules over a division ring
- category of left modules over a ring
- category of locally ringed spaces
- category of M-sets
- category of measurable spaces
- category of metric spaces with continuous maps
- category of metric spaces with ∞ allowed
- category of pairs of sets
- category of pointed sets
- category of pointed topological spaces
- category of posets
- category of prosets
- category of schemes
- category of sets
- category of sets and relations
- category of sets with finite-to-one maps
- category of sheaves
- category of simplicial sets
- category of small categories
- category of smooth manifolds
- category of topological spaces
- category of torsion abelian groups
- category of torsion-free abelian groups
- category of vector spaces
- category of Z-functors
- poset [0,1]
- poset of extended natural numbers
- poset of natural numbers
- trivial category
- walking commutative square
- walking composable pair
- walking isomorphism
- walking morphism