CatDat

Satisfied Properties

Properties from the database

• is abelian
• is essentially countable
• has a generator
• is locally small

Deduced properties

• is essentially small
• has a generating set
• is locally essentially small
• is well-copowered
• is well-powered
• is inhabited
• is additive
• has finite products
• has binary products
• has a terminal object
• has finite powers
• has binary powers
• is connected
• has a multi-terminal object
• is preadditive
• has zero morphisms
• is strongly connected
• has biproducts
• has finite coproducts
• has cokernels
• is conormal
• has kernels
• has equalizers
• has coreflexive equalizers
• is finitely complete
• has pullbacks
• is Cauchy complete
• is unital
• is normal
• is mono-regular
• is balanced
• is regular
• is accessible
• is semi-strongly connected
• has disjoint finite products
• is Malcev
• is pointed
• has an initial object
• is filtered
• is sifted
• has binary coproducts
• has coequalizers
• has reflexive coequalizers
• is finitely cocomplete
• has pushouts
• has finite copowers
• has binary copowers
• has a multi-initial object
• is counital
• has a cogenerating set
• is epi-regular
• is coregular
• is coaccessible
• has disjoint finite coproducts
• is co-Malcev
• is cosifted
• is cofiltered

Unsatisfied Properties

Properties from the database

• does not have a cogenerator
• is not countable
• does not have countable copowers
• does not have countable powers
• is not skeletal
• is not small
• is not split abelian

Deduced properties*

• does not have countable products
• does not have products
• does not have cofiltered limits
• is not complete
• does not have wide pullbacks
• does not have connected limits
• is not essentially finite
• does not have sequential limits
• does not have directed limits
• does not have powers
• is not multi-complete
• is not finite
• is not a groupoid
• is not direct
• is not Grothendieck abelian
• is not discrete
• is not essentially discrete
• is not trivial
• is not thin
• does not have a strict terminal object
• does not have a strict initial object
• is not left cancellative
• is not right cancellative
• is not distributive
• is not countably distributive
• is not infinitary distributive
• is not cartesian closed
• is not extensive
• is not infinitary extensive
• is not one-way
• is not locally multi-presentable
• is not multi-cocomplete
• is not locally finitely multi-presentable
• is not locally poly-presentable
• is not multi-algebraic
• is not locally strongly finitely presentable
• is not finitary algebraic
• is not an elementary topos
• does not have a regular subobject classifier
• does not have a subobject classifier
• is not locally cartesian closed
• is not a Grothendieck topos
• does not have a natural numbers object
• does not have cosifted limits
• does not have countable coproducts
• does not have coproducts
• does not have disjoint coproducts
• does not have filtered colimits
• does not have sifted colimits
• does not have connected colimits
• does not have directed colimits
• does not have exact filtered colimits
• does not have cartesian filtered colimits
• is not locally finitely presentable
• is not finitely accessible
• is not a generalized variety
• is not cocomplete
• is not locally ℵ₁-presentable
• is not locally presentable
• does not have wide pushouts
• does not have sequential colimits
• does not have copowers
• does not have disjoint products
• does not have cocartesian cofiltered limits
• is not infinitary codistributive
• is not countably codistributive
• is not infinitary coextensive
• is not codistributive
• is not cocartesian coclosed
• is not coextensive
• is not inverse
• is not locally copresentable
• does not have a regular quotient object classifier
• does not have a quotient object classifier
• is not locally cocartesian coclosed
• is not self-dual

*This also uses the deduced satisfied properties.