Abstract
In this chapter we will define several important classes of simplicial sets and of maps between simplicial sets by extension and lifting conditions. These include the classical notions of Kan complexes and Kan fibrations, as well as the notion of inner Kan complex (or ∞-category). Kan complexes and Kan fibrations play a central role in homotopy theory and will therefore be of fundamental importance in Part II of this book.
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Heuts, G., Moerdijk, I. (2022). Kan Conditions for Simplicial Sets. In: Simplicial and Dendroidal Homotopy Theory. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, vol 75. Springer, Cham. https://doi.org/10.1007/978-3-031-10447-3_5
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DOI: https://doi.org/10.1007/978-3-031-10447-3_5
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Publisher Name: Springer, Cham
Print ISBN: 978-3-031-10446-6
Online ISBN: 978-3-031-10447-3
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