directed colimits
A category has directed colimits if it has colimits of diagrams indexed by directed (small) posets. This is actually equivalent to having filtered colimits. Directed colimits are (somewhat confusingly) also known as inverse limits.
- Dual property: directed limits
- Related properties: cocomplete, filtered colimits
- nLab Link
Relevant implications
Examples
There are 63 categories with this property.
- category of abelian groups
- category of abelian sheaves
- category of algebras
- category of Banach spaces with linear contractions
- category of commutative algebras
- category of commutative monoids
- category of commutative rings
- category of compact Hausdorff spaces
- category of fields
- category of filtered vector spaces
- category of finite sets and bijections
- category of finite sets and surjections
- category of groups
- category of Hausdorff spaces
- category of Jónsson-Tarski algebras
- category of left modules over a division ring
- category of left modules over a ring
- 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 ∞ allowed
- category of monoids
- category of non-empty sets
- category of pairs of sets
- category of pointed sets
- category of pointed topological spaces
- category of posets
- category of prosets
- category of pseudo-metric spaces with non-expansive maps
- category of rings
- category of rngs
- category of semigroups
- category of sets
- category of sheaves
- category of simplicial sets
- category of small categories
- category of topological spaces
- category of torsion abelian groups
- category of torsion-free abelian groups
- category of vector spaces
- category of Z-functors
- delooping of a non-trivial finite group
- delooping of an infinite countable group
- delooping of an infinite uncountable group
- discrete category on two objects
- dual of the category of sets
- dual of the category of topological spaces
- empty category
- poset [0,1]
- poset of extended natural numbers
- poset of ordinal numbers
- proset of integers w.r.t. divisibility
- trivial category
- walking commutative square
- walking composable pair
- walking coreflexive pair
- walking fork
- walking isomorphism
- walking morphism
- walking parallel pair
- walking span
- walking splitting
Counterexamples
There are 23 categories without this property.
- 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 metric spaces with continuous maps
- category of schemes
- category of sets and relations
- category of sets with finite-to-one maps
- category of smooth manifolds
- delooping of the additive monoid of natural numbers
- delooping of the additive monoid of ordinal numbers
- poset of natural numbers
- simplex category
- walking idempotent
Unknown
There are 0 categories for which the database has no information on whether they satisfy this property.
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