HomotopyGroupoidsAndCrossedComplexesInHigherDimensionalAlgebraHDA 2009-01-31 18:08:23 2009-01-31 18:09:06 Topic the title % almost certainly you want these \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} \subsubsection{Homotopy groupoids and crossed complexes as non-commutative structures in \emph{higher dimensional algebra} (HDA): provide tools for solving local-to-global problems} This is a series of papers that were published in 2004 on ``\PMlinkname{Categorical Structures}{CategoricalAlgebras} for Descent and Galois Theory, Hopf Algebras and Semiabelian Categories.'' that appeared as part of the \emph{Proceedings of the Fields Institute Workshop on \PMlinkname{Categorical Structures}{Categoricalalgebras} for Descent and Galois Theory, Hopf Algebras and Semiabelian Categories}, \cite{FIC2004}. Among these remarkable mathematical contributions is an interesting paper on crossed complexes and homotopy groupoids as non-commutative tools for higher dimensional local-to-global problems. In this paper it was pointed out that \emph{``the structures which enable the full use of crossed complexes as a tool in algebraic topology are substantial, intricate and interrelated''}. These applications of crossed complexes are also closely connected with the concept of \PMlinkname{double groupoid}{HomotopyDoubleGroupoidOfAHausdorffSpace}. \begin{thebibliography}{9} \bibitem{FIC2004} PFIWCS-2004. \emph{Proceedings of the Fields Institute Workshop on \PMlinkname{Categorical Structures}{Categoricalalgebras} for Descent and Galois Theory, Hopf Algebras and Semiabelian Categories}., September 23-28, 2004, published in the \emph{Fields Institute Communications \textbf{43}, (2004)}. \bibitem{RBetal2k4} R. Brown et al. ``Crossed complexes and homotopy groupoids as non-commutative tools for higher dimensional local-to-global problems'', in \emph{Fields Institute Communications \textbf{43}:101-130 (2004)}, (PDF and ps documents at arXiv/ math.AT/0212274). \end{thebibliography}