Implication Details
Assumptions: biproducts
Conclusions: finite coproducts, finite products, zero morphisms
Proof: This holds by definition of biproducts.
Show 42 categories using this implication
- category of combinatorial species
- category of commutative monoids
- category of fields
- category of finite groups
- category of finite ordered sets
- category of finite sets
- category of finite sets and bijections
- category of finite sets and injections
- category of finite sets and surjections
- category of Jónsson-Tarski algebras
- category of metric spaces with non-expansive maps
- category of non-empty sets
- category of pairs of sets
- category of pseudo-metric spaces with non-expansive maps
- category of schemes
- category of semigroups
- category of sets and relations
- category of sets with finite-to-one maps
- category of sheaves
- category of smooth manifolds
- category of Z-functors
- 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
- empty category
- poset [0,1]
- poset of extended natural numbers
- poset of natural numbers
- poset of ordinal numbers
- simplex category
- walking commutative square
- walking composable pair
- walking coreflexive pair
- walking fork
- walking idempotent
- walking morphism
- walking parallel pair
- walking span
- walking splitting