The formalism of Segal sections

Edouard Balzin

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arXiv · 1811.09601

The formalism of Segal sections

Edouard Balzin

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Abstract

Given a family of model categories $\cal E \to \cal C$, we associate to it a homotopical category of derived, or Segal, sections $DSect(\cal C,\cal E)$ that models the higher-categorical sections of the localisation $L\cal E \to \cal C$. The derived sections provide an alternative, strict model for various higher algebra objects appearing in the work of Lurie. We prove a few results concerning the properties of the homotopical category $DSect(\cal C,\cal E)$, and as an example, study its behaviour with respect to the base-change along a select class of functors.

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Edouard Balzin. 2018-11-23. The formalism of Segal sections. https://arxiv.org/abs/1811.09601

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