multi-terminal object
This property refers to the existence of a multi-limit of the empty diagram. A category has a multi-terminal object if and only if each connected component has a terminal object.
- Dual property: multi-initial object
- Related properties: multi-complete, terminal object
- nLab Link
Relevant implications
- connected andmulti-terminal object is equivalent to terminal object
- groupoid andmulti-terminal object implies thin
- multi-complete implies multi-terminal object
- multi-initial object andself-dual implies multi-terminal object
- multi-terminal object andself-dual implies multi-initial object
Examples
There are 57 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 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 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 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 schemes
- category of sets
- category of sets and relations
- category of sheaves
- category of simplicial sets
- category of small categories
- category of smooth manifolds
- category of topological spaces
- category of vector spaces
- category of Z-functors
- discrete category on two objects
- dual of the category of sets
- empty category
- poset [0,1]
- poset of extended natural numbers
- proset of integers w.r.t. divisibility
- simplex category
- trivial category
- walking commutative square
- walking composable pair
- walking isomorphism
- walking morphism
Counterexamples
There are 13 categories without this property.
- category of fields
- category of finite sets and bijections
- category of finite sets and injections
- delooping of a non-trivial finite group
- delooping of an infinite countable group
- delooping of the additive monoid of natural numbers
- delooping of the additive monoid of ordinal numbers
- poset of natural numbers
- poset of ordinal numbers
- walking fork
- walking idempotent
- walking parallel pair
- walking span
Unknown
There are 0 categories for which the database has no information on whether they satisfy this property.
—