Rectification of enriched infinity-categories

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Rectification of enriched infinity-categories. / Haugseng, Rune.

In: Algebraic & Geometric Topology, Vol. 15, 2015, p. 1931–1982.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Haugseng, R 2015, 'Rectification of enriched infinity-categories', Algebraic & Geometric Topology, vol. 15, pp. 1931–1982. https://doi.org/10.2140/agt.2015.15.1931

APA

Haugseng, R. (2015). Rectification of enriched infinity-categories. Algebraic & Geometric Topology, 15, 1931–1982. https://doi.org/10.2140/agt.2015.15.1931

Vancouver

Haugseng R. Rectification of enriched infinity-categories. Algebraic & Geometric Topology. 2015;15:1931–1982. https://doi.org/10.2140/agt.2015.15.1931

Author

Haugseng, Rune. / Rectification of enriched infinity-categories. In: Algebraic & Geometric Topology. 2015 ; Vol. 15. pp. 1931–1982.

Bibtex

@article{0b86e170ad7b421f8634b686983f9b77,
title = "Rectification of enriched infinity-categories",
abstract = "We prove a rectification theorem for enriched infinity-categories: If V is a nice monoidal model category, we show that the homotopy theory of infinity-categories enriched in V is equivalent to the familiar homotopy theory of categories strictly enriched in V. It follows, for example, that infinity-categories enriched in spectra or chain complexes are equivalent to spectral categories and dg-categories. A similar method gives a comparison result for enriched Segal categories, which implies that the homotopy theories of n-categories and (infinity,n)-categories defined by iterated infinity-categorical enrichment are equivalent to those of more familiar versions of these objects. In the latter case we also include a direct comparison with complete n-fold Segal spaces. Along the way we prove a comparison result for fibrewise simplicial localizations potentially of independent use.",
keywords = "math.AT, math.CT, 18D20, 18D50, 55P48, 55U35",
author = "Rune Haugseng",
year = "2015",
doi = "10.2140/agt.2015.15.1931",
language = "English",
volume = "15",
pages = "1931–1982",
journal = "Algebraic and Geometric Topology",
issn = "1472-2747",
publisher = "Geometry & Topology Publications",

}

RIS

TY - JOUR

T1 - Rectification of enriched infinity-categories

AU - Haugseng, Rune

PY - 2015

Y1 - 2015

N2 - We prove a rectification theorem for enriched infinity-categories: If V is a nice monoidal model category, we show that the homotopy theory of infinity-categories enriched in V is equivalent to the familiar homotopy theory of categories strictly enriched in V. It follows, for example, that infinity-categories enriched in spectra or chain complexes are equivalent to spectral categories and dg-categories. A similar method gives a comparison result for enriched Segal categories, which implies that the homotopy theories of n-categories and (infinity,n)-categories defined by iterated infinity-categorical enrichment are equivalent to those of more familiar versions of these objects. In the latter case we also include a direct comparison with complete n-fold Segal spaces. Along the way we prove a comparison result for fibrewise simplicial localizations potentially of independent use.

AB - We prove a rectification theorem for enriched infinity-categories: If V is a nice monoidal model category, we show that the homotopy theory of infinity-categories enriched in V is equivalent to the familiar homotopy theory of categories strictly enriched in V. It follows, for example, that infinity-categories enriched in spectra or chain complexes are equivalent to spectral categories and dg-categories. A similar method gives a comparison result for enriched Segal categories, which implies that the homotopy theories of n-categories and (infinity,n)-categories defined by iterated infinity-categorical enrichment are equivalent to those of more familiar versions of these objects. In the latter case we also include a direct comparison with complete n-fold Segal spaces. Along the way we prove a comparison result for fibrewise simplicial localizations potentially of independent use.

KW - math.AT

KW - math.CT

KW - 18D20, 18D50, 55P48, 55U35

U2 - 10.2140/agt.2015.15.1931

DO - 10.2140/agt.2015.15.1931

M3 - Journal article

VL - 15

SP - 1931

EP - 1982

JO - Algebraic and Geometric Topology

JF - Algebraic and Geometric Topology

SN - 1472-2747

ER -

ID: 145773352