Implication Details
Claim: If a category is additive and has a regular subobject classifier, then it is trivial.
Proof: See MSE/4086192.
This implication has a dual.
Show 47 categories using this implication
- category of abelian groups
- category of large families of abelian groups
- category of finitely generated abelian groups
- category of cochain complexes of abelian groups
- category of F(I)-sets
- category of filtered vector spaces
- category of finite abelian groups
- category of free abelian groups
- category of finitely generated free abelian groups
- category of finitely generated free modules over Z x Z
- category of M-sets
- category of sets with a distinguished subset
- partially ordered set of extended natural numbers
- category of finitely generated projective modules over the ring of dual numbers
- category of quivers
- category of quivers with finite components
- 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 sequences of sets
- category of connected sequences of sets
- category of sets
- category of set functions and commutative squares
- category of countable sets
- category of large families of 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 long transfinite sequences of abelian groups
- 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
- 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