Implication Details
Claim: If a category has a subobject classifier, then it has a regular subobject classifier.
Proof: This is obvious.
This implication has a dual.
Show 53 categories using this implication
- category of abelian groups
- category of large families of abelian groups
- category of finitely generated abelian groups
- category of Banach spaces with linear contractions
- category of commutative monoids
- category of small categories
- category of cochain complexes of abelian groups
- category of compact Hausdorff spaces
- category of F(I)-sets
- 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 Hausdorff spaces
- category of Jónsson-Tarski algebras
- 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 monoids
- category of partially ordered sets
- 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 semigroups
- category of sequences of abelian groups
- category of sequences of sets
- category of connected sequences of sets
- category of sets
- category of pointed 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 empty-or-finite pairs of sets
- category of sheaves
- category of abelian sheaves
- category of combinatorial species
- category of torsion 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
- category of graded abelian groups
- category of graded modules over a graded ring
- category of simplicial sets