On the Krull-Schmidt theorem with application to sheaves

Michael F. Atiyah

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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, $𝒯$ , 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 $𝒯$ 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...