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 .