3 By a 'stable homotopy category' I mean any 'topological' triangulated category.

People often consider exceptional sets of objects (i.e. collections of objects satisfying certain strong orthogonality conditions: $Ext^{l}(P_i,P_j)$ should be zero for $l\neq 0$ + something else) in derived categories of coherent sheaves (over algebraic varieties; possibly the first example corresponds to the Beilnson's description of the derived category of coherent sheaves on the projective space of dimension $n$). Are there any examples of this notion in some stable homotopy categories (in the sense of abstract model categories; one can consider the category of modules over a ring spectrum here)?

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People often consider exceptional sets of objects (i.e. collections of objects satisfying certain strong orthogonality conditions: $Ext^{l}(P_i,P_j)$ should be zero for $l\neq 0$ + something else) in triangulated derived categories of coherent sheaves (over algebraic varieties). varieties; possibly the first example corresponds to the Beilnson's description of the derived category of coherent sheaves on the projective space of dimension $n$). Are there any examples of this notion in some stable homotopy categories?

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# Exceptional collections of objects in topological triangulated categories?

People often consider exceptional sets of objects (i.e. collections of objects satisfying certain strong orthogonality conditions) in triangulated categories of coherent sheaves (over algebraic varieties). Are there any examples of this notion in some stable homotopy categories?