Tensor products and homotopies for ω-groupoids and crossed complexes☆

@inproceedings{Brown1987TensorPA,
  title={Tensor products and homotopies for ω-groupoids and crossed complexes☆},
  author={Ronald Thomas Brown and Philip J. Higgins},
  year={1987}
}

• Ronald Thomas Brown, Philip J. Higgins
• Published 1987
• DOI:10.1016/0022-4049(87)90099-5

Crossed complexes have longstanding uses, explicit and implicit, in homotopy theory and the cohomology of groups. It is here shown that the category of crossed complexes over groupoids has a symmetric monoidal closed structure in which the internal Hom functor is built from morphisms of crossed complexes, nonabelian chain homotopies between them and similar higher homotopies. The tensor product involves non-abelian constructions related to the commutator calculus and the homotopy addition lemma… CONTINUE READING

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