On Deformations of Pasting Diagrams, II

Abstract

We continue the development of the infinitesimal deformation theory of pasting diagrams of k-linear categories begun in Yetter, D.N. "On Deformations of Pasting Diagrams", Theory and Applications of Categories 22 (2009) 24-53. In that paper, the standard result that all obstructions are cocycles was established only for the elementary, composition-free parts of pasting diagrams. In the present work we give a proof for pasting diagrams in general. As tools we use (1) the method developed by Shrestha, in his Kansas State University doctoral dissertation, of representing formulas for obstructions, along with the corresponding cocycle and cobounding conditions by suitably labeled polygons, giving a rigorous exposition of the previously heuristic method, and (2) deformations of pasting diagrams in which some cells are required to be deformed trivially.