Implication Details
Claim: If a category has a quotient object classifier, then it has a regular quotient object classifier.
Proof: This follows from the dual implication.
Show 48 categories using this implication
- category of abelian groups
- category of finitely generated abelian groups
- category of algebras
- category of Banach spaces with linear contractions
- category of commutative algebras
- category of commutative monoids
- category of commutative rings
- category of cochain complexes of abelian groups
- category of compact Hausdorff spaces
- category of finite sets and injections
- category of finite abelian groups
- category of finite ordered sets
- 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 fields of characteristic zero
- category of groups
- category of countable groups
- category of Jónsson-Tarski algebras
- category of M-sets
- category of monoids
- 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 rings
- category of rngs
- category of sequences of abelian groups
- category of sets
- category of set functions and commutative squares
- category of countable sets
- category of set-indexed families of abelian groups
- category of pairs of sets
- category of sheaves
- category of abelian sheaves
- category of combinatorial species
- category of pointed topological spaces
- 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 vector spaces over a large field with a small basis
- category of Z-functors
- category of graded abelian groups
- category of graded modules over a graded ring
- category of simplicial sets