Homotopy groupoids and crossed complexes as non-commutative structures in higher dimensional algebra (HDA): 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].

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.

Bibliography

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).