Properties of categories
Found 142 properties
- is abelian
- is accessible
- is additive
- is balanced
- has binary copowers
- has binary coproducts
- has binary powers
- has binary products
- has biproducts
- is cartesian closed
- has cartesian filtered colimits
- is Cauchy complete
- is co-Malcev
- is coaccessible
- is cocartesian coclosed
- has cocartesian cofiltered limits
- is cocomplete
- is codistributive
- has coequalizers
- is coextensive
- is cofiltered
- has cofiltered limits
- has a cogenerating set
- has a cogenerator
- has cokernels
- is complete
- is connected
- has connected colimits
- has connected limits
- is conormal
- has copowers
- has coproducts
- has coreflexive equalizers
- is coregular
- is cosifted
- has cosifted limits
- is counital
- is countable
- has countable copowers
- has countable coproducts
- has countable powers
- has countable products
- is direct
- has directed colimits
- has directed limits
- is discrete
- has disjoint coproducts
- has disjoint finite coproducts
- has disjoint finite products
- has disjoint products
- is distributive
- is an elementary topos
- is epi-regular
- has equalizers
- is essentially countable
- is essentially discrete
- is essentially finite
- is essentially small
- has exact filtered colimits
- is extensive
- is filtered
- has filtered colimits
- is finitary algebraic
- is finite
- has finite copowers
- has finite coproducts
- has finite powers
- has finite products
- is finitely accessible
- is finitely cocomplete
- is finitely complete
- is a generalized variety
- has a generating set
- has a generator
- is Grothendieck abelian
- is a Grothendieck topos
- is a groupoid
- is infinitary codistributive
- is infinitary coextensive
- is infinitary distributive
- is infinitary extensive
- is inhabited
- has an initial object
- is inverse
- has kernels
- is left cancellative
- is locally cartesian closed
- is locally cocartesian coclosed
- is locally copresentable
- is locally essentially small
- is locally finitely multi-presentable
- is locally finitely presentable
- is locally multi-presentable
- is locally poly-presentable
- is locally presentable
- is locally small
- is locally strongly finitely presentable
- is locally ℵ₁-presentable
- is Malcev
- is mono-regular
- is multi-algebraic
- is multi-cocomplete
- is multi-complete
- has a multi-initial object
- has a multi-terminal object
- is normal
- is one-way
- is pointed
- has powers
- is preadditive
- has products
- has pullbacks
- has pushouts
- has a quotient object classifier
- has reflexive coequalizers
- is regular
- has a regular quotient object classifier
- has a regular subobject classifier
- is right cancellative
- is self-dual
- is semi-strongly connected
- has sequential colimits
- has sequential limits
- is sifted
- has sifted colimits
- is skeletal
- is small
- is split abelian
- has a strict initial object
- has a strict terminal object
- is strongly connected
- has a subobject classifier
- has a terminal object
- is thin
- is trivial
- is unital
- is well-copowered
- is well-powered
- has wide pullbacks
- has wide pushouts
- has zero morphisms
- is ℵ₁-accessible