Two Models for the Homotopy Theory of Cocomplete Homotopy Theories
Two Models for the Homotopy Theory of Cocomplete Homotopy Theories
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DissertationPrüfungsdatum
21.07.2014Datum der Veröffentlichung
06.08.2014Erstgutachter
Schwede, StefanZweitgutachter
Teichner, PeterMetadaten
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Inhalt
There two major approaches to the problem of formalizing the notion of a "homotopy theory", they are homotopical algebra and higher category theory. The main result of this thesis is a precise comparison between these approaches, i.e. the theorem saying that the homotopy theory of cofibration categories (representing homotopical algebra) is equivalent to the homotopy theory of finitely cocomplete quasicategories (representing higher category theory).
Schlagwörter
Homotopietheorie, Kategorientheorie, homotopy theory, category theory
Klassifikation (DDC)
510 MathematikSzumiło, Karol: Two Models for the Homotopy Theory of Cocomplete Homotopy Theories. - Bonn, 2014. - Dissertation, Rheinische Friedrich-Wilhelms-Universität Bonn.
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5n-36923
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5n-36923
@phdthesis{handle:20.500.11811/6136,
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5n-36923,
author = {{Karol Szumiło}},
title = {Two Models for the Homotopy Theory of Cocomplete Homotopy Theories},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2014,
month = aug,
note = {There two major approaches to the problem of formalizing the notion of a "homotopy theory", they are homotopical algebra and higher category theory. The main result of this thesis is a precise comparison between these approaches, i.e. the theorem saying that the homotopy theory of cofibration categories (representing homotopical algebra) is equivalent to the homotopy theory of finitely cocomplete quasicategories (representing higher category theory).},
url = {https://hdl.handle.net/20.500.11811/6136}
}
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5n-36923,
author = {{Karol Szumiło}},
title = {Two Models for the Homotopy Theory of Cocomplete Homotopy Theories},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2014,
month = aug,
note = {There two major approaches to the problem of formalizing the notion of a "homotopy theory", they are homotopical algebra and higher category theory. The main result of this thesis is a precise comparison between these approaches, i.e. the theorem saying that the homotopy theory of cofibration categories (representing homotopical algebra) is equivalent to the homotopy theory of finitely cocomplete quasicategories (representing higher category theory).},
url = {https://hdl.handle.net/20.500.11811/6136}
}
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