Implication details
Claim: If a category has binary products and is inhabited, then it is cosifted.
Proof: This follows from the dual implication.
This implication has a dual.
Show 37 categories using this implication
- discrete category on two objects
- category of abelian groups
- category of finitely generated abelian groups
- category of finite sets and bijections
- category of Banach spaces with linear contractions
- category of sets equipped with an irreflexive binary relation
- category of sets equipped with a symmetric irreflexive binary relation
- category of small categories
- category of coproducts of Euclidean spaces
- category of finite sets and surjections
- category of filtered vector spaces
- category of finite sets of even cardinality
- 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 finitely generated groups
- category of smooth manifolds
- category of extended metric spaces
- category of partially ordered sets
- category of partially ordered sets without isolated points
- category of finitely generated projective modules over the ring of dual numbers
- 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
- discrete category of sets
- category of non-empty sets
- category of empty-or-finite pairs of sets
- category of vector spaces
- walking span