Implication Details
Claim: If a category is coextensive, then it has disjoint finite products and has a strict terminal object.
Proof: This follows from the dual implication.
This implication has a dual.
Show 69 categories using this implication
- category of abelian groups
- category of large families of abelian groups
- category of finitely generated abelian groups
- delooping of the additive monoid of natural numbers
- category of Banach spaces with linear contractions
- category of commutative algebras
- category of commutative monoids
- category of commutative rings
- category of small categories
- category of cochain complexes of abelian groups
- simplex category
- category of F(I)-sets
- category of filtered vector spaces
- 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
- 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 finitely generated free abelian groups
- category of finitely generated free modules over Z x Z
- category of groups
- category of countable groups
- category of metric spaces with non-expansive maps
- category of metric spaces with ∞ allowed
- category of monoids
- category of pseudo-metric spaces with non-expansive maps
- category of partially ordered sets
- category of preordered sets
- category of finitely generated projective modules over the ring of dual numbers
- category of quivers
- category of quivers with finite components
- 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 rngs
- category of schemes
- category of semigroups
- category of sequences of abelian groups
- category of sequences of sets
- category of connected sequences of sets
- category of set functions and commutative squares
- category of countable sets
- category of large families of sets
- category of large families of sets which are mostly singletons
- category of non-empty sets
- category of pairs of sets
- category of empty-or-finite pairs of sets
- category of sheaves
- category of abelian sheaves
- category of combinatorial species
- category of torsion abelian groups
- category of torsion-free abelian groups
- category of long transfinite sequences of abelian groups
- category of vector spaces
- category of countable-dimensional vector spaces
- category of large families of vector spaces which are mostly zero
- category of large vector spaces over a large field with a small basis
- category of finite Z-sets
- category of graded abelian groups
- category of graded modules over a graded ring
- walking coreflexive pair
- walking morphism