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Total cofibres of diagrams of spectra

2005
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New York Journal of Mathematics New York J. Math
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unpublished

If Y is a diagram of spectra indexed by an arbitrary poset C together with a specified sub-poset D, we define the total cofibre Γ(Y) of Y as cofibre(hocolim D (Y) E hocolim C (Y)). We construct a comparison map ˆ Γ Y : holim C Y E hom(Z, ˆ Γ(Y)) to a mapping spectrum of a fibrant replacement of Γ(Y) where Z is a simplicial set obtained from C and D, and characterise those poset pairs D ⊂ C for whichˆΓwhichˆ whichˆΓ Y is a stable equivalence. The characterisation is given in terms of stable

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