CatDat

Properties

Properties from the database

• is discrete
• is finite
• is trivial

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
• is finitary algebraic
• is a Grothendieck topos
• is self-dual
• is split abelian
• has equalizers
• is left cancellative
• has wide pullbacks
• has filtered limits
• has pullbacks
• is Cauchy complete
• has sequential limits
• is locally finitely presentable
• is locally presentable
• is cocomplete
• is complete
• is finitely complete
• has products
• has finite products
• has countable products
• has binary products
• has a terminal object
• is connected
• has a generator
• has exact filtered colimits
• has filtered colimits
• is locally ℵ₁-presentable
• has coproducts
• is an elementary topos
• is cartesian closed
• is infinitary distributive
• is distributive
• has finite coproducts
• has a strict initial object
• has an initial object
• has a subobject classifier
• has disjoint finite coproducts
• has disjoint coproducts
• is epi-regular
• is finitely cocomplete
• has a cogenerator
• is mono-regular
• is abelian
• is additive
• is preadditive
• has zero morphisms
• is pointed
• has coequalizers
• is Grothendieck abelian
• is Malcev
• is inhabited
• is balanced
• has connected colimits
• is right cancellative
• has wide pushouts
• has countable coproducts
• has binary coproducts
• has pushouts
• has a strict terminal object
• has sequential colimits

Non-Properties

Non-Properties from the database

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Deduced Non-Properties*

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*This also uses the deduced properties.