Compact Corigid Objects in Triangulated Categories and Co-t-structures

In the work of Hoshino, Kato and Miyachi, 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. Hoshino, Kato and Miyachi show that such an object yields a non-degenerate t-structure on T whose heart es equivalent to Mod(End(C)^op). Rigid objects in a triangulated category can be 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.

💡 Research Summary

The paper investigates the dual notion to the well‑known construction of t‑structures from compact rigid objects in a triangulated category, as pioneered by Hoshino, Kato and Miyachi. The authors introduce the concept of a corigid object: a compact object S in a triangulated category 𝒯 satisfying Hom𝒯(S