2018/07/04 by Simone Virili, Virili, Simone
Mathematics · Physics and Astronomy · #14F05 #16E30 #16E35 #18E30 #18E35 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #K-Theory and Homology (math.KT) #Nonlinear Waves and Solitons #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1807.01505
openalex publication_date 2018/07/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give a general construction of realization functors for t-structures on the base of a strong stable derivator. In particular, given such a derivator \mathbb D, a t-structure \mathbf t=(\mathcal D≤0,\mathcal D≥0) on the triangulated category \mathbb D(\mathbb 1), and letting \mathcal A=\mathcal D≤0∩ \mathcal D≥0 be its heart, we construct, under mild assumptions, a morphism of prederivators real\mathbf t\colon D\mathcal A→ \mathbb D where D\mathcal A is the natural prederivator enhancing the derived category of \mathcal A. Furthermore, we give criteria for this morphism to be fully faithful and essentially surjective. If the t-structure \mathbf t is induced by a suitably "bounded" co/tilting object, real\mathbf t is an equivalence. Our construction unifies and extends most of the derived co/tilting equivalences appeared in the literature in the last years.