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t-structures on stable (infinity,1)-categories

Titlet-structures on stable (infinity,1)-categories
Publication TypeThesis
Year of Publication2016
AuthorsLoregian, F
Keywordscategory theory, higher category theory, factorization system, torsion theory, homological algebra, higher algebra

The present work re-enacts the classical theory of t-structures reducing the classical definition coming from Algebraic Geometry to a rather primitive categorical gadget: suitable reflective factorization systems (defined in the work of Rosický, Tholen, and Cassidy-Hébert-Kelly), which we call "normal torsion theories" following. A relation between these two objects has previously been noticed by other authors, on the level of the triangulated homotopy categories of stable (infinity,1)-categories. The main achievement of the present thesis is to observe and prove that this relation exists genuinely when the definition is lifted to the higher-dimensional world where the notion of triangulated category comes from.

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Submitted by ( on 2016-06-10T18:05:18Z
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