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Homotopy theory of monoids and derived localization

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Homotopy theory of monoids and derived localization. / Chuang, Joseph; Holstein, Julian; Lazarev, Andrey.
In: Journal of Homotopy and Related Structures, Vol. 16, No. 2, 30.06.2021, p. 175-189.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Chuang, J, Holstein, J & Lazarev, A 2021, 'Homotopy theory of monoids and derived localization', Journal of Homotopy and Related Structures, vol. 16, no. 2, pp. 175-189. https://doi.org/10.1007/s40062-021-00276-6

APA

Chuang, J., Holstein, J., & Lazarev, A. (2021). Homotopy theory of monoids and derived localization. Journal of Homotopy and Related Structures, 16(2), 175-189. https://doi.org/10.1007/s40062-021-00276-6

Vancouver

Chuang J, Holstein J, Lazarev A. Homotopy theory of monoids and derived localization. Journal of Homotopy and Related Structures. 2021 Jun 30;16(2):175-189. Epub 2021 Mar 3. doi: 10.1007/s40062-021-00276-6

Author

Chuang, Joseph ; Holstein, Julian ; Lazarev, Andrey. / Homotopy theory of monoids and derived localization. In: Journal of Homotopy and Related Structures. 2021 ; Vol. 16, No. 2. pp. 175-189.

Bibtex

@article{d8ffbe034c794359bdefea4abdcc40d8,
title = "Homotopy theory of monoids and derived localization",
abstract = "We use derived localization of the bar and nerve constructions to provide simple proofs of a number of results in algebraic topology, both known and new. This includes a recent generalization of Adams{\textquoteright}s cobar-construction to the non-simply connected case, and a new algebraic model for the homotopy theory of connected topological spaces as an ∞-category of discrete monoids.",
keywords = "Cobar-construction, Relative category, Derived localization, Simplicial sets",
author = "Joseph Chuang and Julian Holstein and Andrey Lazarev",
year = "2021",
month = jun,
day = "30",
doi = "10.1007/s40062-021-00276-6",
language = "English",
volume = "16",
pages = "175--189",
journal = "Journal of Homotopy and Related Structures",
issn = "2193-8407",
publisher = "Springer Science + Business Media",
number = "2",

}

RIS

TY - JOUR

T1 - Homotopy theory of monoids and derived localization

AU - Chuang, Joseph

AU - Holstein, Julian

AU - Lazarev, Andrey

PY - 2021/6/30

Y1 - 2021/6/30

N2 - We use derived localization of the bar and nerve constructions to provide simple proofs of a number of results in algebraic topology, both known and new. This includes a recent generalization of Adams’s cobar-construction to the non-simply connected case, and a new algebraic model for the homotopy theory of connected topological spaces as an ∞-category of discrete monoids.

AB - We use derived localization of the bar and nerve constructions to provide simple proofs of a number of results in algebraic topology, both known and new. This includes a recent generalization of Adams’s cobar-construction to the non-simply connected case, and a new algebraic model for the homotopy theory of connected topological spaces as an ∞-category of discrete monoids.

KW - Cobar-construction

KW - Relative category

KW - Derived localization

KW - Simplicial sets

U2 - 10.1007/s40062-021-00276-6

DO - 10.1007/s40062-021-00276-6

M3 - Journal article

VL - 16

SP - 175

EP - 189

JO - Journal of Homotopy and Related Structures

JF - Journal of Homotopy and Related Structures

SN - 2193-8407

IS - 2

ER -