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

Source abstract

Abstract 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, $$\mathcal{T}$$, 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 $$\mathcal{T}$$ 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, $$\mathcal{S}$$, of a triangulated category, $$\mathcal{T}$$, 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($$\mathcal{S}$$)op), and hence an abelian subcategory of $$\mathcal{T}$$.