Compact corigid objects in triangulated categories and co-t-structures

David Pauksztello

Open Mathematics, Tome 6 (2008), p. 25-42 / Harvested from The Polish Digital Mathematics Library

Résumé

In the work of Hoshino, Kato and Miyachi, [11], the authors look at t-structures induced by a compact object, C , of a triangulated category, 𝒯 , which is rigid in the sense of Iyama and Yoshino, [12]. Hoshino, Kato and Miyachi show that such an object yields a non-degenerate t-structure on 𝒯 whose heart is equivalent to Mod(End(C )op). Rigid objects in a triangulated category can the thought of as behaving like chain differential graded algebras (DGAs). Analogously, looking at objects which behave like cochain DGAs naturally gives the dual notion of a corigid object. Here, we see that a compact corigid object, 𝒮 , of a triangulated category, 𝒯 , induces a structure similar to a t-structure which we shall call a co-t-structure. We also show that the coheart of this non-degenerate co-t-structure is equivalent to Mod(End(𝒮 )op), and hence an abelian subcategory of 𝒯 .

Détail

Publié le : 2008-01-01

Zbl 1152.18009

EUDML-ID : urn:eudml:doc:269400

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