2cellsforms
2cellsforms is a term used in some discussions of higher category theory to describe a framework in which two-dimensional morphisms (2-cells) are enriched by differential-form data. In this usage, a bicategory or 2-category is equipped not only with objects, 1-cells, and 2-cells, but also with a graded algebra of differential forms attached to the hom-categories. A 2-cell form can be viewed as a 2-cell paired with a differential form label, and the compositions of 2-cells are required to satisfy compatibility rules that mirror the familiar Leibniz rule from differential geometry.
The formal setup typically includes a bicategory B together with a mechanism that assigns to each hom-category
Examples and applications of the idea are explored in more speculative or exploratory work. In some proposed
Overall, 2cellsforms represents an area at the intersection of higher category theory and differential geometry, intended