empty category
- notation:
- objects: no objects
- morphisms: no morphisms
- nLab Link
This is the category with no objects and no morphisms. It is the initial object in the category of small categories.
Properties
Properties from the database
- has binary products
- is discrete
- is finite
- is preadditive
Deduced properties
- is essentially finite
- is small
- is essentially small
- is locally small
- is locally essentially small
- is well-copowered
- is well-powered
- is essentially discrete
- is skeletal
- is a groupoid
- is thin
- has connected limits
- has equalizers
- is left cancellative
- has pullbacks
- has wide pullbacks
- has filtered limits
- is Cauchy complete
- has sequential limits
- has zero morphisms
- is mono-regular
- is self-dual
- is balanced
- has connected colimits
- has coequalizers
- is right cancellative
- has wide pushouts
- has filtered colimits
- has pushouts
- has sequential colimits
- is epi-regular
- has binary coproducts
Non-Properties
Non-Properties from the database
- is not inhabited
Deduced Non-Properties*
- is not connected
- does not have a terminal object
- does not have finite products
- is not finitely complete
- is not complete
- does not have products
- does not have countable products
- does not have exact filtered colimits
- is not infinitary distributive
- is not distributive
- is not locally presentable
- is not locally finitely presentable
- is not locally ℵ₁-presentable
- is not finitary algebraic
- is not trivial
- does not have disjoint finite coproducts
- does not have disjoint coproducts
- is not an elementary topos
- is not cartesian closed
- is not a Grothendieck topos
- does not have a subobject classifier
- does not have finite coproducts
- is not additive
- is not abelian
- is not Grothendieck abelian
- is not split abelian
- does not have an initial object
- is not pointed
- does not have a strict initial object
- does not have a generator
- is not Malcev
- is not finitely cocomplete
- is not cocomplete
- does not have coproducts
- does not have a strict terminal object
- does not have countable coproducts
- does not have a cogenerator
*This also uses the deduced properties.
Unknown properties
—
Special morphisms
- Isomorphisms: none
- Monomorphisms: none
- Epimorphisms: none