Implication details
Claim: If a category has filtered-colimit-stable monomorphisms, then it has filtered colimits.
Proof: This holds by definition.
This implication has a dual.
Show 48 categories using this implication
- category of finitely generated abelian groups
- delooping of the bicyclic monoid
- delooping of the double bicyclic monoid
- delooping of the additive monoid of natural numbers
- delooping of the additive monoid of ordinal numbers
- simplex category
- category of coproducts of Euclidean spaces
- category of finite sets and injections
- category of finite abelian groups
- category of finite groups
- category of finite ordered sets
- category of finite 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 free abelian groups
- category of finitely generated free abelian groups
- category of finitely generated free modules over Z x Z
- category of countable groups
- category of finitely generated groups
- category of smooth manifolds
- category of measurable spaces
- category of metric spaces with continuous maps
- partially ordered set of 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 with finite components
- category of sets and relations
- category of schemes
- category of countable sets
- category of countably infinite sets
- category of large families of sets which are mostly empty
- category of sets with finite-to-one maps
- category of empty-or-finite pairs of sets
- category of combinatorial species
- category of topological spaces
- category of pointed topological spaces
- category of uniform spaces
- category of countable-dimensional vector spaces
- category of finite Z-sets
- cocompletion of a discrete–pair join
- category of ω-sets
- walking coreflexive pair
- walking idempotent