CatDat

Properties

Properties from the database

• is cartesian closed
• has a cogenerator
• has disjoint coproducts
• is locally finitely presentable
• is locally small

Deduced properties

• is locally essentially small
• has coproducts
• has disjoint finite coproducts
• has finite coproducts
• is distributive
• has finite products
• has binary products
• has a terminal object
• is connected
• has a strict initial object
• has an initial object
• is infinitary distributive
• is locally presentable
• is cocomplete
• is complete
• has connected limits
• has filtered limits
• is finitely complete
• has wide pullbacks
• has equalizers
• has products
• has countable products
• has pullbacks
• is Cauchy complete
• has sequential limits
• has a generator
• is well-copowered
• is well-powered
• has exact filtered colimits
• has filtered colimits
• is locally ℵ₁-presentable
• is inhabited
• has connected colimits
• is finitely cocomplete
• has wide pushouts
• has coequalizers
• has countable coproducts
• has binary coproducts
• has pushouts
• has sequential colimits

Non-Properties

Non-Properties from the database

• is not Malcev
• is not balanced
• is not finitary algebraic
• is not skeletal
• does not have a strict terminal object

Deduced Non-Properties*

• is not discrete
• is not trivial
• is not essentially discrete
• is not pointed
• does not have zero morphisms
• is not thin
• is not essentially small
• is not small
• is not essentially finite
• is not finite
• is not left cancellative
• is not self-dual
• is not preadditive
• is not additive
• is not abelian
• is not Grothendieck abelian
• is not split abelian
• is not a groupoid
• is not mono-regular
• does not have a subobject classifier
• is not an elementary topos
• is not a Grothendieck topos
• is not right cancellative
• is not epi-regular

*This also uses the deduced properties.