CatDat

Satisfied Properties

Properties from the database

• is finitary algebraic
• is a Grothendieck topos
• is locally small
• is semi-strongly connected

Deduced properties

• is locally essentially small
• has a generator
• has a generating set
• is inhabited
• is locally strongly finitely presentable
• is well-copowered
• is regular
• is finitely complete
• has equalizers
• has coreflexive equalizers
• has finite products
• has binary products
• has a terminal object
• has pullbacks
• is Cauchy complete
• has finite powers
• has binary powers
• is connected
• has a multi-terminal object
• is locally finitely presentable
• is locally ℵ₁-presentable
• is locally presentable
• has exact filtered colimits
• has filtered colimits
• has directed colimits
• has cartesian filtered colimits
• is cocomplete
• is finitely accessible
• is ℵ₁-accessible
• is accessible
• is well-powered
• is a generalized variety
• has sifted colimits
• has reflexive coequalizers
• is multi-algebraic
• is locally finitely multi-presentable
• has connected limits
• has wide pullbacks
• is complete
• has products
• has countable products
• has powers
• has countable powers
• has cofiltered limits
• has sequential limits
• is multi-complete
• is locally multi-presentable
• is multi-cocomplete
• is locally poly-presentable
• has coproducts
• is an elementary topos
• is cartesian closed
• is infinitary distributive
• is countably distributive
• has countable coproducts
• is distributive
• has finite coproducts
• has a strict initial object
• has an initial object
• has a subobject classifier
• is mono-regular
• is balanced
• has a regular subobject classifier
• has disjoint finite coproducts
• has disjoint coproducts
• is epi-regular
• is finitely cocomplete
• has a cogenerator
• is infinitary extensive
• is extensive
• has cocartesian cofiltered limits
• is locally cartesian closed
• is coregular
• is co-Malcev
• has a natural numbers object
• is filtered
• is sifted
• has connected colimits
• has cosifted limits
• has copowers
• has binary coproducts
• has coequalizers
• has countable copowers
• has sequential colimits
• has pushouts
• has directed limits
• has wide pushouts
• has finite copowers
• has binary copowers
• has a multi-initial object
• has a cogenerating set
• is cosifted
• is cofiltered

Unsatisfied Properties

Properties from the database

• is not Malcev
• is not skeletal

Deduced properties*

• is not direct
• is not discrete
• is not thin
• does not have a strict terminal object
• is not right cancellative
• is not left cancellative
• is not a groupoid
• is not one-way
• 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 normal
• is not preadditive
• is not additive
• is not abelian
• is not Grothendieck abelian
• is not split abelian
• is not essentially small
• is not small
• is not essentially countable
• is not essentially finite
• is not finite
• is not countable
• is not locally copresentable
• is not strongly connected
• is not unital
• does not have cokernels
• does not have disjoint finite products
• does not have disjoint products
• is not codistributive
• is not countably codistributive
• is not infinitary codistributive
• is not cocartesian coclosed
• is not coextensive
• is not infinitary coextensive
• is not conormal
• is not inverse
• is not coaccessible
• does not have a regular quotient object classifier
• does not have a quotient object classifier
• is not locally cocartesian coclosed
• is not counital
• is not self-dual

*This also uses the deduced satisfied properties.