CatDat

Properties

Properties from the database

• has binary products
• is discrete
• is finite
• is preadditive

Deduced properties

• is essentially finite
• is small
• is essentially small
• is locally small
• is locally essentially small
• is well-copowered
• is well-powered
• is essentially discrete
• is skeletal
• is a groupoid
• is thin
• has connected limits
• has equalizers
• is left cancellative
• has pullbacks
• has wide pullbacks
• has filtered limits
• is Cauchy complete
• has sequential limits
• has zero morphisms
• is mono-regular
• is self-dual
• is balanced
• has connected colimits
• has coequalizers
• is right cancellative
• has wide pushouts
• has filtered colimits
• has pushouts
• has sequential colimits
• is epi-regular
• has binary coproducts

Non-Properties

Non-Properties from the database

• is not inhabited

Deduced Non-Properties*

• is not connected
• does not have a terminal object
• does not have finite products
• is not finitely complete
• is not complete
• does not have products
• does not have countable products
• does not have exact filtered colimits
• is not infinitary distributive
• is not distributive
• is not locally presentable
• is not locally finitely presentable
• is not locally ℵ₁-presentable
• is not finitary algebraic
• is not trivial
• does not have disjoint finite coproducts
• does not have disjoint coproducts
• is not an elementary topos
• is not cartesian closed
• is not a Grothendieck topos
• does not have a subobject classifier
• does not have finite coproducts
• is not additive
• is not abelian
• is not Grothendieck abelian
• is not split abelian
• does not have an initial object
• is not pointed
• does not have a strict initial object
• does not have a generator
• is not Malcev
• is not finitely cocomplete
• is not cocomplete
• does not have coproducts
• does not have a strict terminal object
• does not have countable coproducts
• does not have a cogenerator

*This also uses the deduced properties.