PlanetPhysics/Homotopy Groupoids and Crossed Complexes

Fields Institute Workshop 2004 Topic: Non-commutative Structures in Higher Dimensional Algebra (HDA) that provide Tools for Solving Local-to-Global Problems
This is the topic of a series of papers that were published in 2004 on "Categorical Structures for Descent and Galois Theory, Hopf Algebras and Semiabelian Categories." that appeared as part of the Proceedings of the \htmladdnormallink{fields {http://planetphysics.us/encyclopedia/CosmologicalConstant2.html} Institute Workshop on Categorical Structures for Descent and Galois Theory, Hopf Algebras and Semiabelian categories},.

Homotopy Groupoids and Crossed Complexes
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 "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 double groupoid.