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arXiv · 0802.0800

The ziqqurath of exact sequences of n-groupoids

Giuseppe Metere
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Abstract

Higher Dimensional Categories are showing relevant implications in several fields of mathematical research. Nevertheless basic algebraic tools, in order to further develop the theory, are far from being established. In this thesis we introduce a notion of exactness for exact sequences of pointed n-groupoids. Furthermore we test it generalizing a well known result for (fibrations of) groupoids [R.Brown, 1970]. Namely, given a fibration F of (pointed) groupoids and its strict kernel it is possible to obtain a 6-term exact sequence of groups (of loops) and pointed sets (iso classes of objects). The ziqqurath, aka step-pyramid, comes out from iterating this construction, and it consists in several sequences of n-groupoids, (n-1)-groupoids and so on up to pointed sets (0-groupoids), of increasing length.

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Giuseppe Metere. 2008-02-06. The ziqqurath of exact sequences of n-groupoids. https://arxiv.org/abs/0802.0800

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