Implication Details
Claim: If a category has biproducts, then it has finite coproducts and has finite products and has zero morphisms.
Proof: This holds by definition of biproducts.
Show 50 categories using this implication
- empty category
- discrete category on two objects
- 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 commutative monoids
- simplex category
- category of coproducts of Euclidean spaces
- category of finite sets and injections
- category of finite sets and surjections
- category of finite groups
- category of finite ordered sets
- 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 fields
- category of fields of characteristic zero
- category of Jónsson-Tarski algebras
- category of smooth manifolds
- category of sets with a distinguished subset
- partially ordered set of natural numbers
- partially ordered set of extended natural numbers
- partially ordered collection of ordinal numbers
- category of partially ordered sets without isolated points
- category of sets and relations
- category of schemes
- category of semigroups
- category of set functions and commutative squares
- discrete category of sets
- category of sets with finite-to-one maps
- category of non-empty sets
- category of pairs of sets
- category of sheaves
- category of Z-functors
- cocompletion of a discrete–pair join
- forked commutative square
- real interval [0,1]
- walking commutative square
- walking composable pair
- walking coreflexive pair
- walking fork
- walking idempotent
- walking morphism
- walking parallel pair
- walking span
- walking splitting