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On deformations of pasting diagrams, II

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Tej Shrestha and D. N. Yetter

We continue the development of the infinitesimal deformation theory of
pasting diagrams of $k$-linear categories begun in TAC, Vol 22, #2. In
that article 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 the method developed by Shrestha
of simultaneously 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 deformations of pasting diagrams in which some cells are required to
be deformed trivially.

Keywords:
pasting diagrams, pasting schemes, deformation theory

2010 MSC:
Primary: 18D05, 13D03, Secondary: 18E05

*Theory and Applications of Categories,*
Vol. 29, 2014,
No. 21, pp 569-608.

Published 2014-10-21.

http://www.tac.mta.ca/tac/volumes/29/21/29-21.pdf

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