Implication details
Claim: If a category has pullback-stable regular epimorphisms, then it has pullbacks.
Proof: This holds by definition.
This implication has a dual.
Show 66 categories using this implication
- category of abelian groups
- category of finitely generated abelian groups
- category of Banach spaces with linear contractions
- category of commutative monoids
- category of cochain complexes of abelian groups
- category of compact Hausdorff spaces
- simplex category
- category of coproducts of Euclidean spaces
- category of finite sets and surjections
- category of filtered vector spaces
- category of finite abelian groups
- category of finite groups
- category of finite ordered sets
- category of finite sets of even cardinality
- category of finite sets of odd cardinality
- category of finite sets of cardinality a power of 3
- 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
- category of fields of characteristic zero
- category of free abelian groups
- category of finitely generated free abelian groups
- category of finitely generated free modules over Z x Z
- category of groups
- category of finitely generated groups
- category of smooth manifolds
- category of monoids
- partially ordered set of extended natural numbers
- category of partially ordered sets without isolated points
- 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 sets and relations
- category of rngs
- category of semigroups
- category of sequences of abelian groups
- category of sequences of sets
- category of connected sequences of sets
- category of pointed sets
- category of set functions and commutative squares
- category of countable sets
- category of non-empty sets
- category of pairs of sets
- category of empty-or-finite pairs of sets
- category of abelian sheaves
- category of torsion-free 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
- cocompletion of a discrete–pair join
- forked commutative square
- category of graded abelian groups
- category of graded modules over a graded ring
- category of simplicial sets
- walking composable pair
- walking coreflexive pair
- walking idempotent
- walking morphism
- walking parallel pair
- walking splitting