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.
Show 19 categories using this implication
- category of fields
- category of finite sets and bijections
- category of finite sets and injections
- category of free abelian groups
- category of metric spaces with continuous maps
- category of non-empty sets
- category of semigroups
- category of sets and relations
- category of sets with finite-to-one maps
- category of smooth manifolds
- delooping of a non-trivial finite group
- delooping of an infinite countable group
- delooping of an infinite uncountable group
- delooping of the additive monoid of natural numbers
- delooping of the additive monoid of ordinal numbers
- discrete category on two objects
- walking fork
- walking parallel pair
- walking span