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Let T be a Hom-finite triangulated Krull-Schmidt category over a field k.Inspired by a definition of Koenig and Liu, we say that a family S of pairwiseorthogonal objects in T with trivial endomorphism rings is a simple-mindedsystem if its closure under extensions is all of T. We construct torsion pairsin T associated to any subset X of a simple-minded system S, and use these todefine left and right mutations of S relative to X. When T has a Serre functor\nu, and S and X are invariant under \nu[1], we show that these mutations areagain simple-minded systems. We are particularly interested in the case where Tis the stable module category of a self-injective algebra \Lambda. In thiscase, our mutation procedure parallels that introduced by Koenig and Yang forsimple-minded collections in the derived category of \Lambda. It follows thatthe mutation of the set of simple \Lambda-modules relative to X yields theimages of the simple \Gamma-modules under a stable equivalence between \Gamma\and \Lambda, where \Gamma\ is the tilting mutation of \Lambda\ relative to X.

Torsion pairs and simple-minded systems in triangulated categories