Doubly Weak Double Categories
Abstract
Abstract We propose a definition of double categories whose composition of 1-cells is weak in both directions. Namely, a doubly weak double category is a double computad—a structure with 2-cells of all possible double-categorical shapes—equipped with all possible composition operations, coherently. We also characterize them using “implicit” double categories, which are double computads having all possible compositions of 2-cells, but no compositions of 1-cells; doubly weak double categories are then obtained by a simple representability criterion. Finally, they can also be defined by adding a “tidiness” condition to the double bicategories of Verity, or to the cubical bicategories of Garner.
Fields of Study & Subjects
Homotopy and Cohomology in Algebraic Topology
Logic
programming
and type systems
Reasoning
and Knowledge
Publication details
- Journal / source
- Applied Categorical Structures
- Publisher
- Springer Science and Business Media LLC
- Volume
- 34
- Issue
- 4
- Publication date
- 4 May 2026
- Language
- EN