CatDat

Satisfied Properties

Properties from the database

• has disjoint finite products
• is finitary algebraic
• is locally small
• is Malcev
• has a strict terminal object

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
• is connected
• has pullbacks
• is Cauchy complete
• has finite powers
• has binary powers
• is locally finitely presentable
• is locally presentable
• is locally ℵ₁-presentable
• is cocomplete
• is complete
• has connected limits
• has products
• has countable products
• has wide pullbacks
• has cofiltered limits
• has sequential limits
• has powers
• has countable powers
• is well-powered
• has exact filtered colimits
• has filtered colimits
• has directed colimits
• has connected colimits
• has sifted colimits
• has reflexive coequalizers
• is finitely cocomplete
• has cosifted limits
• has sequential colimits
• has coequalizers
• has coproducts
• has countable coproducts
• has finite coproducts
• has binary coproducts
• has an initial object
• has pushouts
• has directed limits
• has wide pushouts
• has copowers
• has countable copowers
• has finite copowers
• has binary copowers
• has disjoint products

Unsatisfied Properties

Properties from the database

• is not balanced
• is not co-Malcev
• is not codistributive
• does not have a cogenerating set
• is not skeletal
• does not have a strict initial object
• is not strongly connected

Deduced properties*

• is not left cancellative
• is not right cancellative
• is not distributive
• is not infinitary distributive
• is not cartesian closed
• is not extensive
• is not infinitary extensive
• is not lextensive
• is not a groupoid
• is not mono-regular
• is not direct
• is not discrete
• does not have zero morphisms
• does not have biproducts
• is not pointed
• is not preadditive
• is not additive
• is not abelian
• is not Grothendieck abelian
• is not split abelian
• is not essentially discrete
• is not trivial
• is not thin
• does not have disjoint finite coproducts
• does not have disjoint coproducts
• is not one-way
• is not essentially small
• is not small
• is not finite
• is not essentially finite
• is not self-dual
• is not an elementary topos
• does not have a subobject classifier
• does not have a regular subobject classifier
• is not locally cartesian closed
• is not a Grothendieck topos
• is not unital
• is not infinitary codistributive
• is not coextensive
• is not infinitary coextensive
• does not have a cogenerator
• is not epi-regular
• is not inverse
• is not counital

*This also uses the deduced satisfied properties.