Implication Details
Claim: If a category has filtered-colimit-stable monomorphisms, then it has filtered colimits.
Proof: This holds by definition.
Show 27 categories using this implication
- category of combinatorial species
- category of countable groups
- category of countable sets
- category of finite abelian groups
- category of finite groups
- category of finite ordered sets
- category of finite sets
- category of finite sets and injections
- 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 finitely generated abelian groups
- category of free abelian groups
- category of measurable spaces
- category of metric spaces with continuous maps
- category of pointed topological spaces
- category of schemes
- category of sets and relations
- category of sets with finite-to-one maps
- category of smooth manifolds
- category of topological spaces
- delooping of the additive monoid of natural numbers
- delooping of the additive monoid of ordinal numbers
- partially ordered set of natural numbers
- simplex category
- walking coreflexive pair
- walking idempotent