Implication details
Claim: If a category has pushout-stable regular monomorphisms, then it has pushouts.
Proof: This follows from the dual implication.
This implication has a dual.
Show 72 categories using this implication
- category of abelian groups
- category of finitely generated abelian groups
- delooping of the additive monoid of ordinal numbers
- category of Banach spaces with linear contractions
- category of sets equipped with an irreflexive binary relation
- category of sets equipped with a symmetric irreflexive binary relation
- 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 injections
- 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 smooth manifolds
- 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 pseudo-metric spaces with non-expansive maps
- category of partially ordered sets
- category of partially ordered sets without isolated points
- category of preordered sets
- category of finitely generated projective modules over the ring of dual numbers
- 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 schemes
- category of sequences of abelian groups
- category of connected sequences of sets
- category of countable sets
- category of large families of sets which are mostly empty
- category of large families of sets which are mostly singletons
- category of sets with finite-to-one maps
- category of non-empty sets
- category of empty-or-finite pairs of sets
- category of abelian sheaves
- category of topological spaces
- category of pointed topological spaces
- category of torsion-free abelian groups
- category of uniform spaces
- 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
- walking composable pair
- walking coreflexive pair
- walking fork
- walking idempotent
- walking morphism
- walking parallel pair
- walking span
- walking splitting