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

Pauksztello, David (2008) Compact corigid objects in triangulated categories and co-t-structures. Central European Journal of Mathematics, 6 (1). pp. 25-42.

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In the work of Hoshino, Kato and Miyachi, [11], the authors look at t-structures induced by a compact object, CC , of a triangulated category, TT , 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 TT whose heart is equivalent to Mod(End( CC )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, SS , of a triangulated category, TT , 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( SS )op), and hence an abelian subcategory of TT .

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Journal Article
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Central European Journal of Mathematics
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19 Oct 2017 12:30
Last Modified:
22 Nov 2022 05:06