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arXiv · 1608.00483

Homotopy- and Cohomology Groups of Kan Complexes

Jan Steinebrunner
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Abstract

This article shows several new methods for proofs on Kan complexes while using them to give a compact introduction to the homotopy groups of these complexes. Then more advanced objects are studied starting with homology and the Hurewicz homomorphism. Eilenberg-Mac Lane-spaces are constructed explicitly and can then be used to define spectral cohomology. In the end the equivalence to the usual simplicial cohomology is shown.

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Jan Steinebrunner. 2016-08-01. Homotopy- and Cohomology Groups of Kan Complexes. https://arxiv.org/abs/1608.00483

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