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pro vyhledávání: '"Ieke Moerdijk"'
Autor:
Gijs Heuts, Ieke Moerdijk
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
Autor:
Ieke Moerdijk
Publikováno v:
Lecture Notes in Mathematics ISBN: 9783031122439
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https://doi.org/10.1007/978-3-031-12244-6_16
https://doi.org/10.1007/978-3-031-12244-6_16
Autor:
Gijs Heuts, Ieke Moerdijk
Publikováno v:
Simplicial and Dendroidal Homotopy Theory ISBN: 9783031104466
In this chapter we will apply the formalism of Quillen model categories discussed in the previous chapter to the category of simplicial sets. In his first exposition of the theory of model categories, Quillen already showed that the category of simpl
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https://doi.org/10.1007/978-3-031-10447-3_8
https://doi.org/10.1007/978-3-031-10447-3_8
Autor:
Gijs Heuts, Ieke Moerdijk
Publikováno v:
Simplicial and Dendroidal Homotopy Theory ISBN: 9783031104466
The theory of operads is a convenient framework to define various types of algebraic structures in many different contexts. In this first chapter we will define the notion of an operad as well as that of an algebra for an operad. We present several w
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https://doi.org/10.1007/978-3-031-10447-3_1
https://doi.org/10.1007/978-3-031-10447-3_1
Autor:
Gijs Heuts, Ieke Moerdijk
Publikováno v:
Simplicial and Dendroidal Homotopy Theory ISBN: 9783031104466
In this chapterwe study extension conditions for dendroidal sets and lifting conditions for maps of dendroidal sets which parallel the conditions for simplicial sets of the previous chapter. The structure of this chapter follows the same plan to stre
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https://doi.org/10.1007/978-3-031-10447-3_6
https://doi.org/10.1007/978-3-031-10447-3_6
Autor:
Gijs Heuts, Ieke Moerdijk
Publikováno v:
Simplicial and Dendroidal Homotopy Theory ISBN: 9783031104466
In Section 9.5 we introduced the covariant model structure on a slice category dSets/B, for a fixed dendroidal set B. This model category represents the homotopy theory of ‘B-algebras’, as we will see in Section 13.5. The first aim of this chapte
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https://doi.org/10.1007/978-3-031-10447-3_13
https://doi.org/10.1007/978-3-031-10447-3_13
Autor:
Gijs Heuts, Ieke Moerdijk
Publikováno v:
Simplicial and Dendroidal Homotopy Theory ISBN: 9783031104466
In this chapter we will introduce the category of dendroidal sets, which is the main object of study of this book. The definition of a dendroidal set mirrors that of a simplicial set, except that the category Δ is replaced by a larger category Ω of
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https://doi.org/10.1007/978-3-031-10447-3_3
https://doi.org/10.1007/978-3-031-10447-3_3
Autor:
Gijs Heuts, Ieke Moerdijk
Publikováno v:
Simplicial and Dendroidal Homotopy Theory ISBN: 9783031104466
In later chapters we will develop the homotopy theory of simplicial and dendroidal spaces, i.e., diagrams of simplicial sets indexed on the categories Δop and Ωop. There is a standard way of equipping such diagram categories with a model structure
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https://doi.org/10.1007/978-3-031-10447-3_10
https://doi.org/10.1007/978-3-031-10447-3_10
Autor:
Gijs Heuts, Ieke Moerdijk
Publikováno v:
Simplicial and Dendroidal Homotopy Theory ISBN: 9783031104466
In [123] Quillen proposed an axiomatic framework for homotopy theory through the notion of a model structure on a category. Such a structure consists of three distinguished classes of morphisms, calledweak equivalences, fibrations, and cofibrations,
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https://doi.org/10.1007/978-3-031-10447-3_7
https://doi.org/10.1007/978-3-031-10447-3_7
Autor:
Gijs Heuts, Ieke Moerdijk
Publikováno v:
Simplicial and Dendroidal Homotopy Theory ISBN: 9783031104466
In this final chapter we fulfil one of the main promises of this book, namely we prove that the homotopy theory of ∞-operads is equivalent to that of simplicial (or topological) operads. To prepare for this, Sections 14.1 and 14.2 establish some ra
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https://doi.org/10.1007/978-3-031-10447-3_14
https://doi.org/10.1007/978-3-031-10447-3_14