0.0.1 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 fields Institute Workshop on Categorical Structures for Descent and Galois
Theory, Hopf Algebras and Semiabelian categories, [1].
0.1 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.
References
[1] PFIWCS-2004. Proceedings of the Fields Institute Workshop on Categorical
Structures for Descent and Galois Theory, Hopf Algebras and Semiabelian Categories.,
September 23-28, 2004, published in the Fields Institute Communications 43, (2004).
[2] R. Brown et al. “Crossed complexes and homotopy
groupoids as non-commutative tools for higher dimensional local-to-global problems”, in
Fields Institute Communications 43:101-130 (2004), (PDF and ps documents at arXiv/
math.AT/0212274).
