| 书目名称 | Effective Kan Fibrations in Simplicial Sets |
| 编辑 | Benno van den Berg,Eric Faber |
| 视频video | |
| 概述 | Contributes to the emerging area of homotopy type theory.Provides new effective foundations for simplicial homotopy theory.Light on prerequisites (only basic category theory is required) |
| 丛书名称 | Lecture Notes in Mathematics |
| 图书封面 |  |
| 描述 | This book introduces the notion of an effective Kan fibration, a new mathematical structure which can be used to study simplicial homotopy theory. The main motivation is to make simplicial homotopy theory suitable for homotopy type theory. Effective Kan fibrations are maps of simplicial sets equipped with a structured collection of chosen lifts that satisfy certain non-trivial properties. Here it is revealed that fundamental properties of ordinary Kan fibrations can be extended to explicit constructions on effective Kan fibrations. In particular, a constructive (explicit) proof is given that effective Kan fibrations are stable under push forward, or fibred exponentials. Further, it is shown that effective Kan fibrations are local, or completely determined by their fibres above representables, and the maps which can be equipped with the structure of an effective Kan fibration are precisely the ordinary Kan fibrations. Hence implicitly, both notions still describe the same homotopy theory. These new results solve an open problem in homotopy type theory and provide the first step toward giving a constructive account of Voevodsky’s model of univalent type theory in simplicial sets. |
| 出版日期 | Book 2022 |
| 关键词 | Simplicial Sets; Homotopy Theory; Constructive Mathematics; Homotopy Type Theory; Kan Complexes |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-3-031-18900-5 |
| isbn_softcover | 978-3-031-18899-2 |
| isbn_ebook | 978-3-031-18900-5Series ISSN 0075-8434 Series E-ISSN 1617-9692 |
| issn_series | 0075-8434 |
| copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl |
发表于 2025-3-21 17:55:05
