category of finite orders
- notation:
- objects: finite totally ordered sets
- morphisms: order-preserving maps
- Related categories: ,
- nLab Link
This is also known as the augmented simplex category. The finite orders of the form for provide a skeleton (for this includes the empty set).
Satisfied Properties
Properties from the database
- has coequalizers
- has a cogenerator
- is epi-regular
- has equalizers
- is essentially small
- has a generator
- is locally small
- is mono-regular
- has a strict initial object
- is strongly connected
- has a terminal object
Deduced properties
- has coreflexive equalizers
- is connected
- is Cauchy complete
- has an initial object
- is locally essentially small
- is well-copowered
- is well-powered
- has a generating set
- is inhabited
- is balanced
- has reflexive coequalizers
- has a cogenerating set
Unsatisfied Properties
Properties from the database
- does not have binary copowers
- does not have binary powers
- is not essentially finite
- is not one-way
- does not have sequential colimits
- does not have sequential limits
- is not skeletal
- is not small
- does not have a strict terminal object
Deduced properties*
- does not have directed limits
- does not have countable products
- does not have products
- is not complete
- does not have wide pullbacks
- does not have connected limits
- does not have binary products
- does not have finite products
- does not have pullbacks
- is not finitely complete
- does not have finite powers
- does not have countable powers
- does not have powers
- does not have biproducts
- does not have exact filtered colimits
- is not infinitary distributive
- is not distributive
- is not regular
- is not lextensive
- is not finite
- is not a groupoid
- is not direct
- is not thin
- is not left cancellative
- is not discrete
- is not additive
- is not abelian
- is not Grothendieck abelian
- is not split abelian
- is not locally strongly finitely presentable
- is not finitary algebraic
- is not essentially discrete
- is not trivial
- is not pointed
- does not have zero morphisms
- is not preadditive
- is not locally presentable
- is not locally finitely presentable
- is not locally ℵ₁-presentable
- is not cartesian closed
- is not an elementary topos
- does not have a subobject classifier
- does not have a regular subobject classifier
- is not locally cartesian closed
- is not a Grothendieck topos
- is not Malcev
- is not unital
- does not have directed colimits
- does not have filtered colimits
- does not have sifted colimits
- does not have connected colimits
- is not cocomplete
- does not have coproducts
- does not have disjoint coproducts
- is not infinitary extensive
- does not have cofiltered limits
- does not have cosifted limits
- does not have wide pushouts
- does not have countable coproducts
- does not have binary coproducts
- does not have finite coproducts
- does not have disjoint finite coproducts
- is not extensive
- does not have pushouts
- is not finitely cocomplete
- does not have finite copowers
- does not have countable copowers
- does not have copowers
- does not have disjoint products
- does not have disjoint finite products
- is not infinitary codistributive
- is not codistributive
- is not right cancellative
- is not coextensive
- is not infinitary coextensive
- is not coregular
- is not inverse
- is not co-Malcev
- is not counital
- is not self-dual
*This also uses the deduced satisfied properties.
Unknown properties
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Special objects
- terminal object: singleton ordered set
- initial object: empty ordered set
- products: [finite case] direct products with the evident order
Special morphisms
- isomorphisms: bijective order-preserving maps
- monomorphisms: injective order-preserving maps
- epimorphisms: surjective order-preserving maps
- regular monomorphisms: same as monomorphisms
- regular epimorphisms: same as epimorphisms