CatDat

Satisfied Properties

Properties from the database

• has coproducts
• is infinitary codistributive
• is infinitary distributive
• is locally strongly finitely presentable
• is skeletal
• is small
• is strongly connected

Deduced properties

• has finite products
• has binary products
• has a terminal object
• is connected
• is distributive
• has finite coproducts
• has a strict initial object
• has an initial object
• is essentially small
• is locally small
• is locally essentially small
• is well-copowered
• is well-powered
• has a generating set
• is regular
• is finitely complete
• has equalizers
• has pullbacks
• is Cauchy complete
• is locally finitely presentable
• is locally presentable
• is locally ℵ₁-presentable
• is cocomplete
• is complete
• has cofiltered limits
• has connected limits
• has wide pullbacks
• has products
• has countable products
• has sequential limits
• is thin
• is left cancellative
• is cartesian closed
• is locally cartesian closed
• has exact filtered colimits
• has filtered colimits
• has directed colimits
• is inhabited
• has a generator
• is Malcev
• has connected colimits
• is finitely cocomplete
• has wide pushouts
• has countable coproducts
• has binary coproducts
• has sequential colimits
• has coequalizers
• has pushouts
• has directed limits
• is codistributive
• has a strict terminal object
• has a cogenerating set
• is right cancellative
• has a regular subobject classifier
• has a cogenerator
• is coregular
• is co-Malcev

Unsatisfied Properties

Properties from the database

• is not essentially finite
• is not self-dual

Deduced properties*

• is not finite
• is not a groupoid
• is not balanced
• is not mono-regular
• is not abelian
• is not Grothendieck abelian
• is not split abelian
• is not essentially discrete
• is not discrete
• is not trivial
• does not have disjoint finite coproducts
• does not have biproducts
• does not have disjoint coproducts
• is not pointed
• does not have zero morphisms
• is not extensive
• is not infinitary extensive
• is not lextensive
• is not preadditive
• is not additive
• does not have a subobject classifier
• is not an elementary topos
• is not a Grothendieck topos
• is not unital
• does not have disjoint finite products
• does not have disjoint products
• is not coextensive
• is not infinitary coextensive
• is not epi-regular
• is not counital

*This also uses the deduced satisfied properties.