Implication Details
Claim: If a category is additive and has a regular subobject classifier, then it is trivial.
Proof: See MSE/4086192.
Show 32 categories using this implication
- category of abelian groups
- category of finitely generated abelian groups
- category of cochain complexes of abelian groups
- category of filtered vector spaces
- category of finite abelian groups
- category of free abelian groups
- category of M-sets
- category of sets with a distinguished subset
- partially ordered set of extended natural 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 sequences of abelian groups
- category of sets
- category of set functions and commutative squares
- category of countable sets
- category of pairs of sets
- category of sheaves
- category of abelian sheaves
- category of combinatorial species
- category of torsion abelian groups
- category of torsion-free abelian groups
- category of uniform spaces
- category of vector spaces
- preordered set of integers w.r.t. divisibility
- category of graded abelian groups
- category of graded modules over a graded ring
- real interval [0,1]
- category of simplicial sets
- walking commutative square
- walking composable pair
- walking morphism