cofiltered limits
A category has cofiltered limits if it has limits of diagrams indexed by small cofiltered categories. This is actually equivalent to having directed limits.
- Dual property: filtered colimits
- Related properties: cofiltered, complete, cosifted limits, directed limits
- nLab Link
Relevant implications
- biproducts andcofiltered limits implies cocartesian cofiltered limits
- cocartesian coclosed andcofiltered limits implies cocartesian cofiltered limits
- cocartesian cofiltered limits implies cofiltered limits andfinite coproducts
- cofiltered limits andcoreflexive equalizers andpushouts implies cosifted limits
- cofiltered limits andextensive andterminal object implies cocartesian cofiltered limits
- cofiltered limits andfinite powers implies powers
- cofiltered limits andfinite products implies products
- cofiltered limits andself-dual implies filtered colimits
- cosifted limits implies cofiltered limits andcoreflexive equalizers
- directed limits is equivalent to cofiltered limits
- filtered colimits andself-dual implies cofiltered limits
- wide pullbacks is equivalent to cofiltered limits andpullbacks
Examples
There are 52 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 fields
- category of finite sets and bijections
- category of finite sets and injections
- category of groups
- category of Hausdorff spaces
- 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 ∞ allowed
- category of monoids
- category of pairs of sets
- category of pointed sets
- category of pointed topological spaces
- category of posets
- category of prosets
- category of rings
- category of rngs
- category of sets
- category of sheaves
- category of simplicial sets
- category of small categories
- category of topological spaces
- category of vector spaces
- category of Z-functors
- delooping of a non-trivial finite group
- delooping of an infinite countable group
- delooping of the additive monoid of ordinal numbers
- discrete category on two objects
- dual of the category of sets
- empty category
- poset [0,1]
- poset of extended natural numbers
- poset of natural numbers
- poset of ordinal numbers
- proset of integers w.r.t. divisibility
- trivial category
- walking commutative square
- walking composable pair
- walking fork
- walking isomorphism
- walking morphism
- walking parallel pair
- walking span
Counterexamples
There are 18 categories without this property.
- category of combinatorial species
- category of finite abelian groups
- category of finite groups
- category of finite ordered sets
- category of finite sets
- category of finite sets and surjections
- category of finitely generated abelian groups
- category of free abelian groups
- category of metric spaces with continuous maps
- category of metric spaces with non-expansive maps
- category of non-empty sets
- category of pseudo-metric spaces with non-expansive maps
- category of schemes
- category of sets and relations
- category of smooth manifolds
- delooping of the additive monoid 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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