Missing data

Categories with unknown properties

There are 12 categories with at least one unknown property. In total, there are 58 unknown (category, property) pairs.

• category of abelian sheaves (9)
• category of Banach spaces with linear contractions (2)
• category of F(I)-sets (1)
• category of free abelian groups (4)
• category of locally ringed spaces (11)
• category of metric spaces with continuous maps (2)
• category of metric spaces with non-expansive maps (1)
• category of metric spaces with ∞ allowed (1)
• category of pseudo-metric spaces with non-expansive maps (6)
• category of schemes (10)
• category of sheaves (9)
• category of uniform spaces (2)

Functors with unknown properties

There are 0 functors with at least one unknown property. 🎉

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Morphisms with unknown properties

There are 0 morphisms with at least one unknown property. 🎉

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Symmetric monoidal categories with unknown properties

There are 0 symmetric monoidal categories with at least one unknown property. 🎉

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Categories with unknown special morphisms

There are 20 categories with at least one unknown kind of special morphism.

• category of algebras (2)
• category of commutative algebras (1)
• category of commutative monoids (1)
• category of commutative rings (1)
• category of coproducts of Euclidean spaces (2)
• category of finitely generated free modules over Z x Z (2)
• category of locally ringed spaces (3)
• category of metric spaces with continuous maps (1)
• category of metric spaces with non-expansive maps (2)
• category of metric spaces with ∞ allowed (2)
• category of monoids (1)
• category of partially ordered sets (1)
• category of partially ordered sets without isolated points (1)
• category of preordered sets (1)
• category of rings (2)
• category of rngs (2)
• category of schemes (4)
• category of semigroups (1)
• category of small categories (2)
• category of smooth manifolds (2)

Indistinguishable category pairs

There are 14 pairs of categories that cannot be distinguished by the properties currently recorded in the database. This indicates that the data may be incomplete or that a distinguishing property may be missing.

• category of abelian groups ≈ category of left modules over a non-semisimple ring
• category of algebras ≈ category of rings
• category of sets equipped with a binary relation ≈ category of sets equipped with a symmetric binary relation
• category of sets equipped with an irreflexive binary relation ≈ category of sets equipped with a symmetric irreflexive binary relation
• category of sets equipped with a reflexive binary relation ≈ category of sets equipped with a symmetric reflexive binary relation
• category of commutative algebras ≈ category of commutative rings
• category of cochain complexes of abelian groups ≈ category of sequences of abelian groups
• category of cochain complexes of abelian groups ≈ category of graded abelian groups
• category of filtered vector spaces ≈ category of torsion-free abelian groups
• category of Jónsson-Tarski algebras ≈ category of Z-sets
• category of quivers ≈ category of pairs of sets
• category of left modules over a division ring ≈ category of vector spaces
• category of sequences of abelian groups ≈ category of graded abelian groups
• category of sequences of sets ≈ category of set functions and commutative squares

Indistinguishable functor pairs

There are 8 pairs of functors that cannot be distinguished by the properties currently recorded in the database. This indicates that the data may be incomplete or that a distinguishing property may be missing.

• abelianization functor for groups ≈ enveloping group functor
• discrete topology functor ≈ forgetful functor from torsion abelian groups to abelian groups
• empty functor to the category of sets ≈ span endpoints inclusion
• forgetful functor from abelian groups to groups ≈ forgetful functor from commutative rings to rings
• forgetful functor from abelian groups to groups ≈ indiscrete topology functor
• forgetful functor from commutative rings to rings ≈ indiscrete topology functor
• forgetful functor for groups ≈ forgetful functor for vector spaces
• opposite category functor ≈ opposite monoid functor

Indistinguishable symmetric monoidal category pairs

There is 1 pair of symmetric monoidal categories that cannot be distinguished by the properties currently recorded in the database. This indicates that the data may be incomplete or that a distinguishing property may be missing.

• symmetric monoidal category of abelian groups ≈ symmetric monoidal category of modules over a non-absolutely flat commutative ring

Missing category combinations

Among the consistent category property combinations of the form p ∧ ¬q, the following are not yet witnessed by a category in the database or its dual. If some of these combinations are inconsistent, this indicates that some implication is missing.

Missing functor combinations

Every consistent functor property combination of the form p ∧ ¬q is witnessed by a functor in the database or its dual. 🎉

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Missing morphism combinations

Every consistent morphism property combination of the form p ∧ ¬q is witnessed by a morphism in the database or its dual. 🎉

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Missing symmetric monoidal category combinations

Among the consistent symmetric monoidal category property combinations of the form p ∧ ¬q, the following are not yet witnessed by a symmetric monoidal category in the database or its dual. If some of these combinations are inconsistent, this indicates that some implication is missing.