CatDat

Satisfied Properties

Properties from the database

• is finite
• has a generator
• is left cancellative
• is one-way
• is self-dual
• is skeletal
• is strongly connected

Deduced properties

• is essentially finite
• is small
• is essentially small
• is locally small
• is locally essentially small
• is well-copowered
• is well-powered
• has a generating set
• is inhabited
• is Cauchy complete
• has filtered colimits
• has directed colimits
• has coreflexive equalizers
• has reflexive coequalizers
• is direct
• has sequential limits
• is connected
• has sequential colimits
• has cofiltered limits
• has directed limits
• has a cogenerating set
• is inverse
• has a cogenerator
• is right cancellative

Unsatisfied Properties

Properties from the database

• does not have binary products
• does not have equalizers
• does not have an initial object
• does not have pullbacks

Deduced properties*

• does not have finite products
• does not have products
• does not have countable products
• is not complete
• is not finitely complete
• does not have connected limits
• does not have wide pullbacks
• does not have biproducts
• is not pointed
• does not have exact filtered colimits
• is not infinitary distributive
• is not distributive
• does not have a strict initial object
• is not extensive
• is not infinitary extensive
• is not regular
• is not lextensive
• is not a groupoid
• is not balanced
• is not mono-regular
• 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 discrete
• is not trivial
• is not thin
• does not have coequalizers
• does not have zero morphisms
• does not have binary copowers
• 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 binary coproducts
• does not have finite coproducts
• does not have disjoint finite coproducts
• does not have disjoint coproducts
• does not have coproducts
• does not have countable coproducts
• is not cocomplete
• is not finitely cocomplete
• does not have connected colimits
• 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 coextensive
• is not infinitary coextensive
• is not coregular
• does not have binary powers
• does not have finite powers
• does not have countable powers
• does not have powers
• is not epi-regular
• is not co-Malcev
• is not counital
• does not have pushouts
• does not have wide pushouts
• does not have a terminal object
• does not have a strict terminal object

*This also uses the deduced satisfied properties.