CatDat

Properties

Properties from the database

• has disjoint coproducts
• is finitely complete
• is infinitary distributive
• is locally small
• is well-powered

Deduced properties

• is locally essentially small
• has equalizers
• has finite products
• has binary products
• has a terminal object
• has pullbacks
• is connected
• has coproducts
• has disjoint finite coproducts
• has finite coproducts
• is Cauchy complete
• is distributive
• has a strict initial object
• has an initial object
• is inhabited
• has countable coproducts
• has binary coproducts

Non-Properties

Non-Properties from the database

• is not Malcev
• is not cartesian closed
• does not have coequalizers
• does not have countable products
• is not skeletal
• does not have a strict terminal object

Deduced Non-Properties*

• is not discrete
• does not have products
• is not complete
• does not have filtered limits
• does not have wide pullbacks
• does not have connected limits
• is not essentially discrete
• is not trivial
• is not thin
• is not essentially finite
• is not finite
• is not pointed
• does not have zero morphisms
• does not have sequential limits
• is not locally presentable
• is not locally finitely presentable
• is not locally ℵ₁-presentable
• is not finitary algebraic
• is not an elementary topos
• is not a Grothendieck topos
• is not preadditive
• is not additive
• is not abelian
• is not Grothendieck abelian
• is not split abelian
• is not a groupoid
• is not essentially small
• is not small
• is not right cancellative
• is not cocomplete
• is not finitely cocomplete
• does not have pushouts
• does not have connected colimits
• does not have wide pushouts
• is not left cancellative
• is not self-dual

*This also uses the deduced properties.