CatDat

Properties

Properties from the database

• has binary products
• is cocomplete
• has connected limits
• is locally small
• is skeletal
• is thin
• is well-powered

Deduced properties

• is locally essentially small
• has equalizers
• is left cancellative
• has pullbacks
• has wide pullbacks
• has filtered limits
• is Cauchy complete
• has sequential limits
• has coequalizers
• is right cancellative
• has connected colimits
• has filtered colimits
• is finitely cocomplete
• has wide pushouts
• has coproducts
• has finite coproducts
• has countable coproducts
• has binary coproducts
• has an initial object
• has a strict initial object
• has pushouts
• is connected
• is inhabited
• has a generator
• has a cogenerator
• has sequential colimits

Non-Properties

Non-Properties from the database

• does not have a terminal object
• is not well-copowered

Deduced Non-Properties*

• is not essentially small
• is not small
• is not finite
• is not essentially finite
• is not trivial
• is not essentially discrete
• is not discrete
• is not a groupoid
• does not have finite products
• is not finitely complete
• is not complete
• does not have products
• does not have disjoint finite coproducts
• does not have disjoint coproducts
• is not pointed
• does not have zero morphisms
• does not have countable products
• does not have exact filtered colimits
• is not infinitary distributive
• is not distributive
• is not cartesian closed
• 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
• does not have a subobject classifier
• is not preadditive
• is not additive
• is not abelian
• is not Grothendieck abelian
• is not split abelian
• is not balanced
• is not mono-regular
• is not Malcev
• does not have a strict terminal object
• is not epi-regular
• is not self-dual

*This also uses the deduced properties.