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 the 2-category of 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.
Keywords: pasting diagrams, pasting schemes, deformation theory
2000 MSC: Primary: 18D05, 13D03, Secondary: 18E05
Theory and Applications of Categories,
Vol. 22, 2009,
No. 2, pp 24-53.
http://www.tac.mta.ca/tac/volumes/22/2/22-02.dvi
http://www.tac.mta.ca/tac/volumes/22/2/22-02.ps
http://www.tac.mta.ca/tac/volumes/22/2/22-02.pdf
ftp://ftp.tac.mta.ca/pub/tac/html/volumes/22/2/22-02.dvi
ftp://ftp.tac.mta.ca/pub/tac/html/volumes/22/2/22-02.ps