finitely complete
A category is finitely complete when every finite diagram has a limit.
- Dual property: finitely cocomplete
- Related properties: complete, equalizers, finite products
- nLab Link
Relevant implications
- additive andfinitely complete implies Malcev
- biproducts andfinitely complete andpointed implies unital
- coequalizers andfinitely complete andlocally cartesian closed implies regular
- complete implies cofiltered limits andconnected limits andfinitely complete andwide pullbacks
- elementary topos is equivalent to cartesian closed andfinitely complete andsubobject classifier
- exact filtered colimits implies filtered colimits andfinitely complete
- finitely cocomplete andself-dual implies finitely complete
- finitely complete andright cancellative implies regular subobject classifier
- finitely complete andself-dual implies finitely cocomplete
- finitely complete andthin implies Malcev
- finitely complete andthin implies regular
- finitely complete is equivalent to equalizers andfinite products
- lextensive is equivalent to extensive andfinitely complete
- Malcev implies finitely complete
- regular subobject classifier implies finitely complete
- regular implies finitely complete
- subobject classifier implies finitely complete andmono-regular
- unital implies finitely complete andpointed
Examples
There are 46 categories with this property.
- category of abelian groups
- category of abelian sheaves
- category of algebras
- category of Banach spaces with linear contractions
- category of combinatorial species
- category of commutative algebras
- category of commutative monoids
- category of commutative rings
- category of finite abelian groups
- category of finite sets
- category of finitely generated abelian groups
- category of free abelian groups
- 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 continuous maps
- category of metric spaces with non-expansive maps
- category of metric spaces with ∞ allowed
- category of monoids
- category of pairs of sets
- category of pointed sets
- category of posets
- category of prosets
- category of rings
- category of rngs
- category of schemes
- 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
- dual of the category of sets
- poset [0,1]
- poset of extended natural numbers
- proset of integers w.r.t. divisibility
- trivial category
- walking commutative square
- walking composable pair
- walking isomorphism
- walking morphism
Counterexamples
There are 19 categories without this property.
- category of fields
- category of finite orders
- category of finite sets and bijections
- category of finite sets and injections
- category of finite sets and surjections
- category of non-empty sets
- category of sets and relations
- category of smooth manifolds
- delooping of a non-trivial finite group
- delooping of an infinite group
- delooping of the additive monoid of natural numbers
- delooping of the additive monoid of ordinal numbers
- discrete category on two objects
- empty category
- poset of natural numbers
- poset of ordinal numbers
- walking fork
- walking parallel pair of morphisms
- walking span
Unknown
There are 0 categories for which the database has no information on whether they satisfy this property.
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