We characterize $t$-structures in stable ∞-categories as suitable quasicategorical factorization systems. More precisely we show that a $t$-structure $\mathcal{t}$ on a stable $\infty$-category $\mathbb{C}$ is equivalent to a normal torsion theory $\mathbf{F}$ on $\mathbb{C}$, i.e. to a factorization system $\mathbf{F} = (\mathcal{\epsilon}, \mathcal{M})$ where both classes satisfy the 3-for-2 cancellation property, and a certain compatibility with pullbacks/pushouts.

%B Applied Categorical Structures %V 24 %P 181–208 %8 Apr %G eng %U https://doi.org/10.1007/s10485-015-9393-z %R 10.1007/s10485-015-9393-z %0 Thesis %D 2016 %T t-structures on stable (infinity,1)-categories %A Fosco Loregian %K category theory, higher category theory, factorization system, torsion theory, homological algebra, higher algebra %X 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. %I SISSA %G en %U http://urania.sissa.it/xmlui/handle/1963/35202 %1 35477 %2 Mathematics %4 1 %# MAT/03 %$ Submitted by floregi@sissa.it (floregi@sissa.it) on 2016-06-10T18:05:18Z No. of bitstreams: 1 main-w.pdf: 1321458 bytes, checksum: b705aee6a0652769f8d48ad2ec750e94 (MD5)