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arXiv · 1003.1342

Algebraic models for higher categories

Thomas Nikolaus
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Abstract

We introduce the notion of algebraic fibrant objects in a general model category and establish a (combinatorial) model category structure on algebraic fibrant objects. Based on this construction we propose algebraic Kan complexes as an algebraic model for oo-groupoids and algebraic quasi-categories as an algebraic model for (oo,1)-categories. We furthermore give an explicit proof of the homotopy hypothesis.

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Thomas Nikolaus. 2011-05-30. Algebraic models for higher categories. https://arxiv.org/abs/1003.1342

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