CatDat

Satisfied Properties

Properties from the database

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Deduced properties

• is balanced
• has binary copowers
• has binary coproducts
• has binary powers
• has binary products
• has cartesian filtered colimits
• is Cauchy complete
• is coaccessible
• is cocartesian coclosed
• has cocartesian cofiltered limits
• is cocomplete
• is codistributive
• has coequalizers
• is coextensive
• is cofiltered
• has cofiltered limits
• has a cogenerating set
• has a cogenerator
• is complete
• is connected
• has connected colimits
• has connected limits
• has copowers
• has coproducts
• has coreflexive equalizers
• is coregular
• is cosifted
• has cosifted limits
• has countable copowers
• has countable coproducts
• has countable powers
• has countable products
• is countably codistributive
• has directed colimits
• has directed limits
• has disjoint finite products
• has disjoint products
• is epi-regular
• has equalizers
• is filtered
• has filtered colimits
• has finite copowers
• has finite coproducts
• has finite powers
• has finite products
• is finitely cocomplete
• is finitely complete
• has a generating set
• has a generator
• is infinitary codistributive
• is infinitary coextensive
• is inhabited
• has an initial object
• is locally cocartesian coclosed
• is locally copresentable
• is locally essentially small
• is locally small
• is Malcev
• is mono-regular
• is multi-cocomplete
• is multi-complete
• has a multi-initial object
• has a multi-terminal object
• has powers
• has products
• has pullbacks
• has pushouts
• has a quotient object classifier
• has reflexive coequalizers
• is regular
• has a regular quotient object classifier
• is semi-strongly connected
• has sequential colimits
• has sequential limits
• is sifted
• has sifted colimits
• has a strict terminal object
• has a terminal object
• is well-copowered
• is well-powered
• has wide pullbacks
• has wide pushouts

Unsatisfied Properties

Properties from the database

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Deduced properties*

• is not abelian
• is not accessible
• is not additive
• does not have biproducts
• is not cartesian closed
• is not co-Malcev
• does not have cokernels
• is not conormal
• is not counital
• is not countable
• is not countably distributive
• is not direct
• is not discrete
• does not have disjoint coproducts
• does not have disjoint finite coproducts
• is not distributive
• is not essentially countable
• is not essentially discrete
• is not essentially finite
• is not essentially small
• is not extensive
• is not finite
• is not a groupoid
• is not infinitary distributive
• is not infinitary extensive
• is not inverse
• does not have kernels
• is not left cancellative
• is not locally cartesian closed
• is not locally presentable
• is not normal
• is not one-way
• is not pointed
• is not preadditive
• does not have a regular subobject classifier
• is not right cancellative
• is not self-dual
• is not skeletal
• is not small
• is not split abelian
• does not have a strict initial object
• is not strongly connected
• does not have a subobject classifier
• is not thin
• is not trivial
• is not unital
• does not have zero morphisms
• is not Grothendieck abelian
• is not locally ℵ₁-presentable
• is not locally finitely presentable
• is not locally strongly finitely presentable
• is not finitary algebraic
• is not finitely accessible
• is not ℵ₁-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
• is not a Grothendieck topos
• does not have a natural numbers object

*This also uses the deduced satisfied properties.