partial order [0,1]
- notation:
- objects: real numbers between and
- morphisms: a unique morphism when
- nLab Link
- Related categories:
Every partial order can be regarded as a thin category. This is a specific example. This category is locally -presentable (in fact, every object is -presentable), but not locally finitely presentable (in fact, only is finitely presentable).
Properties
Properties from the database
- is cartesian closed
- is locally ℵ₁-presentable
- is self-dual
- is skeletal
- is small
Deduced properties
- is essentially small
- is locally small
- is locally essentially small
- is well-copowered
- is well-powered
- is locally presentable
- is cocomplete
- is complete
- has connected limits
- has filtered limits
- is finitely complete
- has wide pullbacks
- has equalizers
- has products
- is thin
- is left cancellative
- has finite products
- has countable products
- has binary products
- has a terminal object
- has pullbacks
- is connected
- is Cauchy complete
- has sequential limits
- has a generator
- is inhabited
- is Malcev
- has coequalizers
- is right cancellative
- has a cogenerator
- has connected colimits
- has filtered colimits
- is finitely cocomplete
- has wide pushouts
- has coproducts
- is infinitary distributive
- is distributive
- has finite coproducts
- has a strict initial object
- has an initial object
- has countable coproducts
- has binary coproducts
- has pushouts
- has a strict terminal object
- has sequential colimits
Non-Properties
Non-Properties from the database
- is not essentially finite
- is not locally finitely presentable
Deduced Non-Properties*
- is not finite
- is not trivial
- is not essentially discrete
- is not discrete
- is not a groupoid
- is not pointed
- does not have zero morphisms
- does not have disjoint finite coproducts
- does not have disjoint coproducts
- is not finitary algebraic
- is not an elementary topos
- does not have a subobject classifier
- is not a Grothendieck topos
- is not preadditive
- is not additive
- is not abelian
- is not Grothendieck abelian
- is not split abelian
- is not balanced
- is not mono-regular
- is not epi-regular
*This also uses the deduced properties.
Unknown properties
For these properties the database currently doesn't have an answer if they are satisfied or not. Please help to complete the data!
Special morphisms
- Isomorphisms: only the identity morphisms
- Monomorphisms: every morphism
- Epimorphisms: every morphism