CatDat

Properties

Properties from the database

• has a cogenerator
• is an elementary topos
• is essentially small
• has a generator
• is locally small

Deduced properties

• is locally essentially small
• is well-copowered
• is well-powered
• is cartesian closed
• is finitely complete
• has equalizers
• has finite products
• has binary products
• has a terminal object
• has pullbacks
• is connected
• is Cauchy complete
• has a subobject classifier
• has disjoint finite coproducts
• has finite coproducts
• is distributive
• has a strict initial object
• has an initial object
• is epi-regular
• is finitely cocomplete
• is mono-regular
• is inhabited
• is balanced
• has coequalizers
• has binary coproducts
• has pushouts

Non-Properties

Non-Properties from the database

• is not Malcev
• does not have sequential colimits
• does not have sequential limits
• is not skeletal
• is not small
• does not have a strict terminal object

Deduced Non-Properties*

• is not finite
• is not discrete
• does not have countable products
• 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 pointed
• does not have zero morphisms
• is not thin
• is not essentially finite
• is not left cancellative
• is not locally presentable
• is not locally finitely presentable
• is not locally ℵ₁-presentable
• is not finitary algebraic
• is not a Grothendieck topos
• does not have coproducts
• does not have disjoint coproducts
• is not infinitary distributive
• is not preadditive
• is not additive
• is not abelian
• is not Grothendieck abelian
• is not split abelian
• is not a groupoid
• is not right cancellative
• is not cocomplete
• does not have filtered colimits
• does not have exact filtered colimits
• does not have wide pushouts
• does not have connected colimits
• does not have countable coproducts
• is not self-dual

*This also uses the deduced properties.