CatDat

Categories with unknown properties

There are 24 categories that have some unknown properties.

• category of abelian sheaves (5)
• category of algebras (1)
• category of Banach spaces with linear contractions (3)
• category of combinatorial species (2)
• category of Hausdorff spaces (10)
• category of locally ringed spaces (13)
• category of M-sets (1)
• category of measurable spaces (5)
• category of metric spaces with continuous maps (3)
• category of metric spaces with non-expansive maps (2)
• category of metric spaces with ∞ allowed (3)
• category of rings (1)
• category of rngs (1)
• category of schemes (9)
• category of sets and relations (2)
• category of sheaves (7)
• category of simplicial sets (2)
• category of small categories (1)
• category of smooth manifolds (3)
• category of Z-functors (8)
• dual of the category of sets (7)
• poset [0,1] (1)
• poset of extended natural numbers (1)
• walking parallel pair (2)

Categories with properties without recorded reason

There are 12 categories with properties (satisfied or unsatisfied) that have no reason specified.

• category of combinatorial species (4)
• category of finite sets and injections (3)
• category of finite sets and surjections (5)
• category of Hausdorff spaces (1)
• category of locally ringed spaces (1)
• category of measurable spaces (1)
• category of metric spaces with continuous maps (1)
• category of metric spaces with non-expansive maps (3)
• category of metric spaces with ∞ allowed (1)
• category of schemes (1)
• category of simplicial sets (1)
• category of smooth manifolds (5)

Categories with unknown special morphisms

There are 23 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 (2)
• category of commutative monoids (2)
• category of commutative rings (1)
• category of free abelian groups (2)
• category of Hausdorff spaces (1)
• category of left modules over a division ring (3)
• category of locally ringed spaces (4)
• category of measurable spaces (1)
• 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 rings (2)
• category of rngs (2)
• category of schemes (4)
• category of sets and relations (2)
• category of small categories (2)
• category of smooth manifolds (2)
• dual of the category of sets (5)

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

Missing combinations

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

Functors with unknown properties

There are 2 categories that have some unknown properties.

• covariant power set functor (1)
• free group functor (2)