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The Homotopy Theory of (∞,1)-Categories
Norwegian University of Science and Technology, Faculty of Natural Sciences and Technology, Department of Physics.
2014 (English)MasteroppgaveStudent thesis
Abstract [en]

The homotopy category of a stable (∞,1)-category can be endowed with a triangulated structure. The main objective of this thesis is to give a proof of this fact. First it will be discussed some ideas of higher category theory, before (∞,1)-categories and models of (∞,1)-categories will be studied. In particular, topological categories and simplicial categories will be mentioned, but the main focus will be on quasi-categories, which all are models for (∞,1)-categories. The theory of (∞,1)-categories, which is required in order to define stable (∞,1)-categories, is then discussed, in particular functors, subcategories, join constructions, undercategories, overcategories, initial objects, terminal objects, limits and colimits are formally discussed for quasi-categories. Finally, the definition of a stable (∞,1)-category will be discussed. Then the main theorem will be proved, after the required properties of stable (∞,1)-categories are discussed. Background theory from ordinary categories and simplicial sets are collected in the appendices.

Place, publisher, year, edition, pages
Institutt for matematiske fag , 2014. , 146 p.
URN: urn:nbn:no:ntnu:diva-24362Local ID: ntnudaim:10294OAI: diva2:707878
Available from: 2014-03-25 Created: 2014-03-25 Last updated: 2014-03-25Bibliographically approved

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