Structures
Browse a comprehensive collection of categories and functors, each with detailed descriptions, proofs of their properties, and related structures.
A comprehensive and searchable database of categorical structures and their properties
CatDat provides a growing collection of categories and functors. Built by and for those who love category theory.
Properties
Browse a collection of properties of categories and properties of functors, each with relevant results, structures satisfying or not satisfying this property, and related properties.
Deduction System
Category implications and functor implications leverage a deduction system that automatically deduces satisfied and unsatisfied properties from given ones.
Search by properties
Search for categories and functors that satisfy specific properties while not satisfying others. Inconsistent property combinations are detected.
Compare structures
Compare categories and functors directly to identify structural similarities and differences in their properties.
Community-driven
This open-source project welcomes contributions to fill in missing data or observe new combinations of properties.