Implication Details
Claim: If a category is extensive, then it has disjoint finite coproducts and has a strict initial object.
Proof: These are Prop. 2.6 and 2.8 in Introduction to extensive and distributive categories by Carboni-Lack-Walters.
Show 55 categories using this implication
- trivial category
- category of abelian groups
- category of finitely generated abelian groups
- delooping of the additive monoid of natural numbers
- category of small categories
- category of cochain complexes of abelian groups
- category of compact Hausdorff spaces
- category of finite sets and injections
- category of filtered vector spaces
- category of finite abelian groups
- category of finite sets
- 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 free abelian groups
- category of Hausdorff spaces
- category of Jónsson-Tarski algebras
- category of locally ringed spaces
- category of M-sets
- category of smooth manifolds
- category of measurable spaces
- category of metric spaces with continuous maps
- category of metric spaces with ∞ allowed
- category of sets with a distinguished subset
- category of partially ordered sets
- category of preordered sets
- category of left modules over a ring
- category of left modules over a division ring
- category of left modules over a non-semisimple ring
- category of sets and relations
- category of schemes
- category of sequences of abelian groups
- category of sets
- category of pointed sets
- category of set functions and commutative squares
- category of countable sets
- category of sets with finite-to-one maps
- category of non-empty sets
- category of pairs of sets
- category of sheaves
- category of abelian sheaves
- category of combinatorial species
- category of topological spaces
- category of pointed topological spaces
- category of torsion abelian groups
- category of torsion-free abelian groups
- category of uniform spaces
- category of vector spaces
- category of Z-functors
- category of graded abelian groups
- category of graded modules over a graded ring
- category of simplicial sets
- walking isomorphism
- walking morphism