CatDat

Categories with unknown properties

There are 13 categories where at least one property is unknown. In total, there are 83 unknown (category, property)-pairs.

• category of abelian sheaves (12)
• category of Banach spaces with linear contractions (8)
• category of commutative monoids (1)
• category of free abelian groups (2)
• category of locally ringed spaces (8)
• category of measurable spaces (10)
• category of metric spaces with continuous maps (3)
• category of metric spaces with non-expansive maps (6)
• category of metric spaces with ∞ allowed (2)
• category of pseudo-metric spaces with non-expansive maps (7)
• category of schemes (9)
• category of sheaves (9)
• category of Z-functors (6)

Functors with unknown properties

There are 0 functors where at least one property is unknown. 🎉

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Categories with unknown special morphisms

There are 21 categories where at least one type of special morphism is unknown.

• category of algebras (2)
• category of Banach spaces with linear contractions (1)
• category of commutative algebras (1)
• category of commutative monoids (1)
• category of commutative rings (1)
• category of free abelian groups (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 posets (1)
• category of prosets (1)
• category of pseudo-metric spaces with non-expansive maps (1)
• category of rings (2)
• category of rngs (2)
• category of schemes (4)
• category of semigroups (1)
• category of sets and relations (2)
• category of small categories (2)
• category of smooth manifolds (2)

Undistinguishable category pairs

There are 4 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 ring
• category of algebras ≈ category of rings
• category of commutative algebras ≈ category of commutative rings
• category of left modules over a division ring ≈ category of vector spaces

Undistinguishable functor pairs

There are 2 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
• forgetful functor for groups ≈ forgetful functor for vector spaces

Missing category combinations

Among the consistent category 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

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