CatDat

Satisfied Properties

Properties from the database

• is infinitary extensive
• is locally small
• has pullbacks
• has a terminal object
• is well-powered

Deduced properties

• has binary products
• has finite products
• has equalizers
• has coreflexive equalizers
• is finitely complete
• is Cauchy complete
• has finite powers
• has binary powers
• is connected
• has a multi-terminal object
• has coproducts
• is extensive
• has finite coproducts
• has disjoint finite coproducts
• has disjoint coproducts
• has a strict initial object
• has an initial object
• is distributive
• is infinitary distributive
• is countably distributive
• has countable coproducts
• is locally essentially small
• has a natural numbers object
• is inhabited
• is filtered
• is sifted
• has copowers
• has binary coproducts
• has countable copowers
• has finite copowers
• has binary copowers
• has a multi-initial object
• is cosifted
• is cofiltered

Unsatisfied Properties

Properties from the database

• is not balanced
• does not have countable powers
• does not have a generating set
• is not Malcev
• does not have pushouts
• is not semi-strongly connected
• is not skeletal

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 cartesian closed
• is not essentially small
• is not small
• is not finite
• is not essentially countable
• is not countable
• does not have a generator
• is not finitary algebraic
• is not a groupoid
• is not mono-regular
• is not normal
• is not direct
• is not thin
• does not have a strict terminal object
• is not right cancellative
• is not left cancellative
• is not one-way
• is not abelian
• is not Grothendieck abelian
• is not split abelian
• is not discrete
• is not essentially discrete
• is not trivial
• is not pointed
• does not have zero morphisms
• does not have kernels
• does not have biproducts
• is not preadditive
• is not additive
• is not accessible
• is not locally presentable
• is not locally ℵ₁-presentable
• is not locally finitely presentable
• is not locally strongly finitely presentable
• is not ℵ₁-accessible
• is not finitely accessible
• is not a generalized variety
• is not locally multi-presentable
• is not locally finitely multi-presentable
• is not locally poly-presentable
• is not multi-algebraic
• is not an elementary topos
• does not have a subobject classifier
• is not locally cartesian closed
• is not a Grothendieck topos
• is not strongly connected
• is not unital
• does not have cosifted limits
• does not have coequalizers
• does not have reflexive coequalizers
• does not have sifted colimits
• does not have connected colimits
• is not cocomplete
• is not finitely cocomplete
• does not have cokernels
• does not have wide pushouts
• is not multi-cocomplete
• 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 infinitary coextensive
• is not codistributive
• is not cocartesian coclosed
• is not coextensive
• is not coregular
• is not epi-regular
• is not conormal
• is not inverse
• is not locally copresentable
• does not have a quotient object classifier
• does not have a regular quotient object classifier
• is not locally cocartesian coclosed
• is not co-Malcev
• is not counital
• is not self-dual

*This also uses the deduced satisfied properties.