On Deformations of Pasting Diagrams

Details On Deformations of Pasting Diagrams On Deformations of Pasting Diagrams

2007-09-24

arxiv.org/abs/0709.3778v2

Mathematics

Category Theory

31 pages

Scientific paper

We adapt the work of Power to describe general, not-necessarily composable, not-necessarily commutative 2-categorical pasting diagrams and their composable and commutative parts. We provide a deformation theory for pasting diagrams valued in $k$-linear categories, paralleling that provided for diagrams of algebras by Gerstenhaber and Schack, proving the standard results. Along the way, the construction gives rise to a bicategorical analog of the homotopy G-algebras of Gerstenhaber and Voronov.

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