category of metric spaces with non-expansive maps
- notation:
- objects: metric spaces
- morphisms: non-expansive maps , meaning for all
- nLab Link
- Related categories: ,
Properties
Properties from the database
- has binary products
- has coequalizers
- has a cogenerator
- has equalizers
- has filtered colimits
- has a generator
- is locally small
- has a strict initial object
- has a terminal object
- is well-powered
Deduced properties
- is locally essentially small
- has finite products
- is finitely complete
- has pullbacks
- is connected
- has an initial object
- is Cauchy complete
- is inhabited
- has sequential colimits
Non-Properties
Non-Properties from the database
- is not Malcev
- is not balanced
- is not cartesian closed
- is not essentially small
- does not have exact filtered colimits
- does not have finite coproducts
- does not have sequential limits
- is not skeletal
- does not have a strict terminal object
Deduced Non-Properties*
- is not small
- is not finite
- is not essentially finite
- is not discrete
- is not trivial
- is not essentially discrete
- does not have disjoint finite coproducts
- does not have disjoint coproducts
- is not pointed
- does not have zero morphisms
- does not have countable products
- does not have products
- is not complete
- does not have filtered limits
- does not have wide pullbacks
- does not have connected limits
- is not distributive
- is not infinitary distributive
- is not locally presentable
- is not locally finitely presentable
- is not locally ℵ₁-presentable
- is not finitary algebraic
- is not an elementary topos
- is not a Grothendieck topos
- is not preadditive
- is not additive
- is not abelian
- is not Grothendieck abelian
- is not split abelian
- is not a groupoid
- is not mono-regular
- does not have a subobject classifier
- is not thin
- is not left cancellative
- is not right cancellative
- is not finitely cocomplete
- is not cocomplete
- does not have coproducts
- does not have binary coproducts
- does not have pushouts
- does not have wide pushouts
- does not have connected colimits
- does not have countable coproducts
- is not epi-regular
- is not self-dual
*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: bijective isometries
- Monomorphisms: injective non-expansive maps
- Epimorphisms:
Comments
- Once we know how the epimorphism look like (probably the non-expansive maps with dense image), it should follow that it is well-copowered.