Implication Details
Claim: If a category is finitary algebraic, then it is regular.
Proof: The regular epimorphisms are precisely the sort-wise surjective homomorphisms, which are clearly stable under pullbacks.
Show 36 categories using this implication
- category of algebras
- category of commutative algebras
- category of commutative monoids
- category of commutative rings
- category of small categories
- simplex category
- category of groups
- category of Hausdorff spaces
- category of Jónsson-Tarski algebras
- category of locally ringed spaces
- category of M-sets
- category of measurable spaces
- category of metric spaces with non-expansive maps
- category of metric spaces with continuous maps
- category of metric spaces with ∞ allowed
- category of monoids
- partially ordered set of extended natural numbers
- category of pseudo-metric spaces with non-expansive maps
- category of partially ordered sets
- category of preordered sets
- category of rings
- category of rngs
- category of semigroups
- category of sets
- category of pointed sets
- category of set functions and commutative squares
- category of non-empty sets
- category of pairs of sets
- category of topological spaces
- category of pointed topological spaces
- forked commutative square
- category of simplicial sets
- walking commutative square
- walking composable pair
- walking coreflexive pair
- walking morphism