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Book
Effective kan fibrations in simplicial sets
Authors: ---
ISBN: 3031189000 3031188993 Year: 2022 Publisher: Cham, Switzerland : Springer,


Book
Lectures on homotopy theory
Author:
ISBN: 9780444892386 0444892389 9786611754624 1281754625 0080872824 9780080872827 9781281754622 6611754628 Year: 1992 Volume: 171 Publisher: Amsterdam ; New York : North-Holland,

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Abstract

The central idea of the lecture course which gave birth to this book was to define the homotopy groups of a space and then give all the machinery needed to prove in detail that the nth homotopy group of the sphere Sn, for n greater than or equal to 1 is isomorphic to the group of the integers, that the lower homotopy groups of Sn are trivial and that the third homotopy group of S2 is also isomorphic to the group of the integers. All this was achieved by discussing H-spaces and CoH-spaces, fibrations and cofibrations


Book

Book
Simplicial and dendroidal homotopy theory
Authors: ---
ISBN: 3031104471 3031104463 Year: 2022 Publisher: Cham Springer Nature

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Abstract

This open access book offers a self-contained introduction to the homotopy theory of simplicial and dendroidal sets and spaces. These are essential for the study of categories, operads, and algebraic structure up to coherent homotopy. The dendroidal theory combines the combinatorics of trees with the theory of Quillen model categories. Dendroidal sets are a natural generalization of simplicial sets from the point of view of operads. In this book, the simplicial approach to higher category theory is generalized to a dendroidal approach to higher operad theory. This dendroidal theory of higher operads is carefully developed in this book. The book also provides an original account of the more established simplicial approach to infinity-categories, which is developed in parallel to the dendroidal theory to emphasize the similarities and differences. Simplicial and Dendroidal Homotopy Theory is a complete introduction, carefully written with the beginning researcher in mind and ideally suited for seminars and courses. It can also be used as a standalone introduction to simplicial homotopy theory and to the theory of infinity-categories, or a standalone introduction to the theory of Quillen model categories and Bousfield localization.


Book
Homotopy theory and arithmetic geometry : motivic and diophantine aspects, LMS-CMI Research School, London, July 2018
Authors: ---
ISBN: 3030789772 3030789764 Year: 2021 Publisher: Cham, Switzerland : Springer,

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