Missing data
This page lists some missing data in the database. Please help us fill in the gaps by contributing to this project.
Categories with unknown properties
There are 13 categories that have some unknown properties.
- category of combinatorial species
- category of free abelian groups
- category of locally ringed spaces
- category of measurable spaces
- category of metric spaces with continuous maps
- category of schemes
- category of sets and relations
- category of simplicial sets
- category of smooth manifolds
- category of Z-functors
- delooping of the additive monoid of ordinal numbers
- partial order [0,1]
- partial order of extended natural numbers
In total, there are 69 unknown properties of categories.
Categories with unknown special morphisms
- category of commutative rings
- category of locally ringed spaces
- category of metric spaces with ∞ allowed
- category of metric spaces with continuous maps
- category of metric spaces with non-expansive maps
- category of monoids
- category of rings
- category of rngs
- category of schemes
- category of smooth manifolds
Missing combinations
Among the consistent combinations of the form P ∧ ¬Q the following 248 combinations are currently not yet witnessed by an example category (or its dual) in our database. Please help us fill in the gaps by contributing to this project. Please also report in case some combination is inconsistent. This means that an implication is missing in the database.
- is small, but is not left cancellative
- is small, but is not right cancellative
- is small, but is not Cauchy complete
- is complete, but is not well-copowered
- is complete, but does not have binary coproducts
- is complete, but does not have coequalizers
- is complete, but does not have filtered colimits
- is complete, but does not have sequential colimits
- is complete, but does not have connected colimits
- is complete, but does not have pushouts
- is complete, but does not have wide pushouts
- is cocomplete, but is not well-powered
- is cocomplete, but does not have binary products
- is cocomplete, but does not have equalizers
- is cocomplete, but does not have filtered limits
- is cocomplete, but does not have sequential limits
- is cocomplete, but does not have connected limits
- is cocomplete, but does not have pullbacks
- is cocomplete, but does not have wide pullbacks
- is cartesian closed, but is not locally essentially small
- is cartesian closed, but is not well-powered
- is cartesian closed, but is not well-copowered
- is cartesian closed, but does not have coequalizers
- is cartesian closed, but does not have pushouts
- is cartesian closed, but does not have a generator
- is cartesian closed, but is not Cauchy complete
- has zero morphisms, but is not locally small
- has zero morphisms, but is not locally essentially small
- has zero morphisms, but is not well-powered
- has zero morphisms, but is not well-copowered
- has zero morphisms, but does not have binary products
- has zero morphisms, but does not have binary coproducts
- is preadditive, but is not locally small
- is preadditive, but is not well-powered
- is preadditive, but is not well-copowered
- is preadditive, but does not have binary products
- is preadditive, but does not have binary coproducts
- is preadditive, but is not Cauchy complete
- is additive, but is not locally small
- is additive, but is not well-powered
- is additive, but is not well-copowered
- is additive, but is not Cauchy complete
- is additive, but is not Malcev
- is abelian, but is not locally small
- is abelian, but is not well-powered
- is abelian, but is not well-copowered
- is finitely complete, but is not well-copowered
- is finitely cocomplete, but is not well-powered
- is pointed, but is not locally small
- is pointed, but is not locally essentially small
- is pointed, but is not well-powered
- is pointed, but is not well-copowered
- is pointed, but does not have finite products
- is pointed, but does not have finite coproducts
- is pointed, but does not have binary products
- is pointed, but does not have binary coproducts
- is pointed, but does not have disjoint finite coproducts
- is locally finitely presentable, but is not locally small
- is locally presentable, but is not locally small
- is locally presentable, but is not locally ℵ₁-presentable
- is locally ℵ₁-presentable, but is not locally small
- is an elementary topos, but is not locally essentially small
- is an elementary topos, but is not well-powered
- is an elementary topos, but is not well-copowered
- is an elementary topos, but does not have a generator
- is an elementary topos, but does not have a cogenerator
- is a Grothendieck topos, but is not locally small
- is a Grothendieck topos, but is not locally finitely presentable
- is a Grothendieck topos, but is not locally ℵ₁-presentable
- is a Grothendieck topos, but is not finitary algebraic
- is a Grothendieck topos, but does not have exact filtered colimits
- has an initial object, but is not well-powered
- has a terminal object, but is not well-copowered
- has products, but is not well-copowered
- has coproducts, but is not well-powered
- has finite products, but is not well-copowered
- has finite coproducts, but is not well-powered
- has countable products, but is not well-copowered
- has countable coproducts, but is not well-powered
- has filtered limits, but is not Cauchy complete
- has filtered colimits, but is not Cauchy complete
- has sequential limits, but is not Cauchy complete
- has sequential colimits, but is not Cauchy complete
- has a strict initial object, but is not well-powered
- has a strict initial object, but is not Cauchy complete
- has a strict terminal object, but is not locally presentable
- has a strict terminal object, but is not locally ℵ₁-presentable
- has a strict terminal object, but is not well-copowered
- has a strict terminal object, but is not Cauchy complete
- has a strict terminal object, but is not Malcev
- is self-dual, but is not locally small
- is self-dual, but is not locally essentially small
- is self-dual, but is not well-powered
- is self-dual, but is not well-copowered
- is a groupoid, but is not locally small
- is a groupoid, but is not locally essentially small
- is a groupoid, but is not essentially small
- is essentially small, but is not Cauchy complete
- is thin, but is not locally small
- is thin, but is not locally essentially small
- is thin, but does not have pullbacks
- is thin, but does not have pushouts
- is discrete, but is not small
- is discrete, but is not essentially small
- is discrete, but is not finite
- is discrete, but is not essentially finite
- is essentially discrete, but is not small
- is essentially discrete, but is not locally small
- is essentially discrete, but is not essentially small
- is essentially discrete, but is not finite
- is essentially discrete, but is not essentially finite
- is finitary algebraic, but is not locally small
- is finite, but does not have filtered limits
- is finite, but does not have filtered colimits
- is finite, but does not have sequential limits
- is finite, but does not have sequential colimits
- is finite, but is not self-dual
- is finite, but is not left cancellative
- is finite, but is not right cancellative
- is finite, but is not Cauchy complete
- is essentially finite, but is not small
- is essentially finite, but is not locally small
- is essentially finite, but does not have filtered limits
- is essentially finite, but does not have filtered colimits
- is essentially finite, but does not have sequential limits
- is essentially finite, but does not have sequential colimits
- is essentially finite, but is not self-dual
- is essentially finite, but is not finite
- is essentially finite, but is not left cancellative
- is essentially finite, but is not right cancellative
- is essentially finite, but is not Cauchy complete
- has pullbacks, but is not Cauchy complete
- has pushouts, but is not Cauchy complete
- is trivial, but is not small
- is trivial, but is not locally small
- is trivial, but is not finite
- has a subobject classifier, but is not locally essentially small
- has a subobject classifier, but is not finitely cocomplete
- has a subobject classifier, but is not well-powered
- has a subobject classifier, but is not well-copowered
- has a subobject classifier, but does not have an initial object
- has a subobject classifier, but does not have finite coproducts
- has a subobject classifier, but does not have binary coproducts
- has a subobject classifier, but does not have coequalizers
- has a subobject classifier, but does not have pushouts
- has a subobject classifier, but does not have a generator
- has a subobject classifier, but does not have a cogenerator
- has a subobject classifier, but does not have disjoint finite coproducts
- has a subobject classifier, but is not epi-regular
- is balanced, but is not well-powered
- is balanced, but is not well-copowered
- is balanced, but is not Cauchy complete
- is balanced, but is not mono-regular
- is balanced, but is not epi-regular
- is infinitary distributive, but is not finitely complete
- is infinitary distributive, but is not well-powered
- is infinitary distributive, but is not well-copowered
- is infinitary distributive, but does not have equalizers
- is infinitary distributive, but does not have filtered colimits
- is infinitary distributive, but does not have sequential colimits
- is infinitary distributive, but does not have pullbacks
- is infinitary distributive, but does not have a generator
- is infinitary distributive, but is not Cauchy complete
- is distributive, but is not well-powered
- is distributive, but is not well-copowered
- is distributive, but does not have a generator
- is distributive, but is not Cauchy complete
- has exact filtered colimits, but is not complete
- has exact filtered colimits, but is not cocomplete
- has exact filtered colimits, but is not finitely cocomplete
- has exact filtered colimits, but is not well-powered
- has exact filtered colimits, but is not well-copowered
- has exact filtered colimits, but does not have an initial object
- has exact filtered colimits, but does not have products
- has exact filtered colimits, but does not have coproducts
- has exact filtered colimits, but does not have finite coproducts
- has exact filtered colimits, but does not have binary coproducts
- has exact filtered colimits, but does not have countable products
- has exact filtered colimits, but does not have countable coproducts
- has exact filtered colimits, but does not have coequalizers
- has exact filtered colimits, but does not have filtered limits
- has exact filtered colimits, but does not have sequential limits
- has exact filtered colimits, but does not have connected limits
- has exact filtered colimits, but does not have connected colimits
- has exact filtered colimits, but does not have pushouts
- has exact filtered colimits, but does not have a generator
- has exact filtered colimits, but does not have wide pullbacks
- has exact filtered colimits, but does not have wide pushouts
- is Grothendieck abelian, but is not locally small
- is Grothendieck abelian, but is not locally finitely presentable
- is Grothendieck abelian, but is not locally ℵ₁-presentable
- is Grothendieck abelian, but is not finitary algebraic
- has disjoint finite coproducts, but is not well-powered
- has disjoint finite coproducts, but is not well-copowered
- has disjoint finite coproducts, but does not have a terminal object
- has disjoint finite coproducts, but does not have finite products
- has disjoint finite coproducts, but does not have binary products
- has disjoint coproducts, but is not well-powered
- has disjoint coproducts, but is not well-copowered
- has disjoint coproducts, but does not have a terminal object
- has disjoint coproducts, but does not have finite products
- has disjoint coproducts, but does not have binary products
- has disjoint coproducts, but does not have sequential colimits
- has disjoint coproducts, but does not have a generator
- has wide pullbacks, but is not Cauchy complete
- has wide pushouts, but is not Cauchy complete
- is split abelian, but is not locally small
- is split abelian, but is not complete
- is split abelian, but is not cocomplete
- is split abelian, but is not locally finitely presentable
- is split abelian, but is not locally presentable
- is split abelian, but is not locally ℵ₁-presentable
- is split abelian, but is not well-powered
- is split abelian, but is not well-copowered
- is split abelian, but does not have products
- is split abelian, but does not have coproducts
- is split abelian, but does not have countable products
- is split abelian, but does not have countable coproducts
- is split abelian, but does not have filtered limits
- is split abelian, but does not have filtered colimits
- is split abelian, but does not have sequential limits
- is split abelian, but does not have sequential colimits
- is split abelian, but does not have connected limits
- is split abelian, but does not have connected colimits
- is split abelian, but is not finitary algebraic
- is split abelian, but does not have a generator
- is split abelian, but does not have a cogenerator
- is split abelian, but does not have exact filtered colimits
- is split abelian, but is not Grothendieck abelian
- is split abelian, but does not have disjoint coproducts
- is split abelian, but does not have wide pullbacks
- is split abelian, but does not have wide pushouts
- is mono-regular, but is not well-powered
- is mono-regular, but is not well-copowered
- is mono-regular, but is not Cauchy complete
- is mono-regular, but is not epi-regular
- is epi-regular, but is not well-powered
- is epi-regular, but is not well-copowered
- is epi-regular, but is not Cauchy complete
- is epi-regular, but is not mono-regular
- is skeletal, but is not Cauchy complete
- is Malcev, but is not locally small
- is Malcev, but is not locally essentially small
- is Malcev, but is not well-powered
- is Malcev, but is not well-copowered
- is Malcev, but does not have an initial object
- is Malcev, but does not have finite coproducts
- is Malcev, but does not have binary coproducts