Implication Details
Claim: If a category has biproducts and is finitely complete, then it is unital.
Proof: For all objects the canonical morphism is an isomorphism, hence a strong epimorphism.
This implication has a dual.
Show 47 categories using this implication
- trivial category
- category of abelian groups
- category of finitely generated abelian groups
- category of Banach spaces with linear contractions
- category of sets equipped with a reflexive binary relation
- category of sets equipped with a symmetric reflexive binary relation
- category of commutative monoids
- category of small categories
- category of cochain complexes of abelian groups
- category of finite abelian groups
- category of finite sets
- 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 M-sets
- category of metric spaces with non-expansive maps
- category of metric spaces with continuous maps
- category of metric spaces with ∞ allowed
- category of pseudo-metric spaces with non-expansive maps
- category of partially ordered sets
- category of preordered sets
- 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 sequences of abelian groups
- category of connected sequences of sets
- category of sets
- category of pointed sets
- category of countable sets
- category of large families of sets which are mostly singletons
- indiscrete category of sets
- category of abelian sheaves
- category of combinatorial species
- category of pointed topological spaces
- category of vector spaces
- category of countable-dimensional vector spaces
- category of large families of vector spaces which are mostly zero
- category of large vector spaces over a large field with a small basis
- category of finite Z-sets
- category of Z-sets
- category of graded abelian groups
- category of graded modules over a graded ring
- category of simplicial sets
- walking isomorphism