CatDat

Categories with unknown properties

There are 30 categories where at least one property is unknown. In total, there are 152 unknown (category, property)-pairs.

• category of abelian sheaves (12)
• category of Banach spaces with linear contractions (4)
• category of combinatorial species (1)
• category of finite groups (1)
• category of finite ordered sets (2)
• category of finite sets and bijections (3)
• category of finite sets and injections (1)
• category of finite sets and surjections (4)
• category of free abelian groups (3)
• category of Hausdorff spaces (12)
• category of locally ringed spaces (29)
• category of M-sets (1)
• category of measurable spaces (11)
• category of metric spaces with continuous maps (4)
• category of metric spaces with non-expansive maps (8)
• category of metric spaces with ∞ allowed (3)
• category of non-empty sets (1)
• category of pseudo-metric spaces with non-expansive maps (8)
• category of schemes (12)
• category of sets and relations (2)
• category of sets with finite-to-one maps (1)
• category of sheaves (11)
• category of small categories (1)
• category of Z-functors (7)
• delooping of a non-trivial finite group (1)
• delooping of an infinite countable group (3)
• delooping of the additive monoid of natural numbers (1)
• simplex category (2)
• walking fork (2)
• walking parallel pair (1)

Categories with unknown special morphisms

There are 22 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 Hausdorff spaces (1)
• 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 pseudo-metric spaces with non-expansive maps (2)
• 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)

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 or its dual category. 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)