COMPACT COCHAIN OBJECTS IN TRIANGULATED CATEGORIES AND CO-t-STRUCTURES

In the work of Hoshino, Kato and Miyachi, [8], 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, [9]. 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)). 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 tstructure 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)), and hence an abelian subcategory of T . 0. Introduction In [8], Hoshino, Kato and Miyachi consider t-structures induced by compact objects of triangulated categories. Suppose T is a triangulated category with suspension functor Σ : T → T . Hoshino, Kato and Miyachi consider a compact object S of T which satisfies the property HomT (S,Σ S) = 0 for all i > 0. Following the terminology of Iyama and Yoshino, we refer to such an object S as rigid ; see [9]. The two halves of the t-structure in [8] are given by: T 60 = {X ∈ T | HomT (S,Σ X) = 0 for i > 0} T >0 = {X ∈ T | HomT (S,Σ X) = 0 for i < 0}. Recall that a differential graded algebra (DGA) R is called a chain DGA if H (R) = 0 for all i > 0. Moreover, given a DG R-module M we have H (M) ∼= HomD(R)(R,Σ M) for all i ∈ Z; where D(R) denotes the derived category of R. Thus, the object S considered in [8] is analogous to a chain DGA and the two halves of the induced t-structure are