Abstract
In this chapter we review the most important techniques used in this work, which are multi-simplicial techniques. Although known in the literature, we present them in a way that is most suitable for the development of the Segal-type models. We discuss multi-simplicial objects and their Segal maps, and we also introduce the higher categorical notions of n-fold category and strict n-category, as well as their multi-nerves. We provide a multi-simplicial description of these structures. This description is important to build the intuition around the Segal-type models. We also introduce notational conventions that will be used throughout this work.
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Paoli, S. (2019). Multi-Simplicial Techniques. In: Simplicial Methods for Higher Categories. Algebra and Applications, vol 26. Springer, Cham. https://doi.org/10.1007/978-3-030-05674-2_2
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DOI: https://doi.org/10.1007/978-3-030-05674-2_2
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