CatDat

Satisfied Properties

Properties from the database

• has binary products
• is discrete
• is finite
• is multi-algebraic
• is preadditive
• is small

Deduced properties

• has binary powers
• is essentially small
• is locally small
• has a generating set
• is locally essentially small
• is well-copowered
• is well-powered
• is countable
• is essentially finite
• is essentially countable
• has zero morphisms
• is direct
• is one-way
• is skeletal
• is thin
• has sequential limits
• has reflexive coequalizers
• is essentially discrete
• is a groupoid
• has directed limits
• is left cancellative
• is Cauchy complete
• is finitely accessible
• has coreflexive equalizers
• has equalizers
• has pullbacks
• has kernels
• has wide pullbacks
• has connected limits
• has cofiltered limits
• is mono-regular
• is self-dual
• is locally cartesian closed
• is balanced
• is normal
• is ℵ₁-accessible
• is accessible
• has filtered colimits
• has sifted colimits
• has directed colimits
• is locally multi-presentable
• is multi-cocomplete
• is locally finitely multi-presentable
• is locally poly-presentable
• is a generalized variety
• has cosifted limits
• has sequential colimits
• has a multi-initial object
• has a cogenerating set
• is epi-regular
• has pushouts
• has wide pushouts
• is right cancellative
• is locally cocartesian coclosed
• is conormal
• is inverse
• has connected colimits
• has coequalizers
• has cokernels
• has binary copowers
• is coaccessible
• has binary coproducts
• is multi-complete
• has a multi-terminal object

Unsatisfied Properties

Properties from the database

• is not inhabited

Deduced properties*

• does not have a generator
• does not have coproducts
• does not have disjoint coproducts
• is not infinitary distributive
• is not infinitary extensive
• is not finitary algebraic
• is not Grothendieck abelian
• is not trivial
• does not have disjoint finite coproducts
• is not extensive
• is not connected
• does not have a terminal object
• does not have finite products
• does not have products
• does not have countable products
• is not complete
• is not finitely complete
• does not have finite powers
• does not have countable powers
• does not have powers
• does not have finite coproducts
• does not have biproducts
• does not have exact filtered colimits
• does not have cartesian filtered colimits
• is not countably distributive
• is not distributive
• is not regular
• is not additive
• is not abelian
• is not split abelian
• is not locally strongly finitely presentable
• is not locally finitely presentable
• is not cocomplete
• is not locally ℵ₁-presentable
• is not locally 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 a Grothendieck topos
• does not have a natural numbers object
• is not semi-strongly connected
• is not strongly connected
• is not Malcev
• is not unital
• is not sifted
• is not filtered
• is not finitely cocomplete
• does not have an initial object
• is not pointed
• does not have a strict initial object
• does not have countable coproducts
• 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
• does not have cocartesian cofiltered limits
• is not infinitary codistributive
• is not countably codistributive
• is not codistributive
• does not have a strict terminal object
• is not coextensive
• is not infinitary coextensive
• is not coregular
• does not have a cogenerator
• is not locally copresentable
• is not cocartesian coclosed
• does not have a quotient object classifier
• does not have a regular quotient object classifier
• is not co-Malcev
• is not counital
• is not cosifted
• is not cofiltered

*This also uses the deduced satisfied properties.