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On the cogeneration of t-structures

Research paper by M. J. Souto Salorio

Indexed on: 01 Aug '04Published on: 01 Aug '04Published in: Archiv der Mathematik



Abstract

Let C be a set of objects in a triangulated compactly generated category \( \textsf{T}. \) We denote by \( {\cal U}_C\,(_C{\cal U}) \) the smallest suspended subcategory closed under coproducts which contains C (the smallest cosuspended subcategory closed under products which contains C). We prove that if C is a set of compacts objects then \( ({^{\perp}}_{T_{C}I}{\cal U}, \, _{T_{C}I}{\cal U}[1]), \) is a t-structure in \( \textsf{T}, \) where TCI is the dual of C with respect to an injective cogenerator I in the category Mod C. Moreover, we show that: C is a tilting set if and only if \( {\cal U}_C^{\perp}[1] = _{T_{C}I}\cal U. \) And, this is equivalent to TCI is a cotilting object in \( \textsf{T}. \)