Implication details
Claim: If a category has binary coproducts and is inhabited, then it is sifted.
Proof: The category is inhabited by assumption, and the coproduct of two objects is initial in the corresponding category of cospans.
This implication has a dual.
Show 43 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
- delooping of a group
- delooping of an infinite countable group
- delooping of a non-trivial finite group
- delooping of an infinite uncountable group
- delooping of the additive monoid of natural numbers
- delooping of the additive monoid of ordinal numbers
- 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 finite sets and injections
- category of filtered vector spaces
- 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 fields
- category of fields of characteristic zero
- category of free abelian groups
- category of finitely generated free abelian groups
- category of finitely generated free modules over Z x Z
- category of smooth manifolds
- 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 semigroups
- category of sets and bijections
- discrete category of sets
- category of large families of sets and bijections
- category of sets with finite-to-one maps
- category of non-empty sets
- category of abelian sheaves
- category of vector spaces
- category of countable-dimensional vector spaces
- forked commutative square
- walking fork
- walking parallel pair
- walking span