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Correspondences and stable homotopy theory (2211.05589v2)
Published 10 Nov 2022 in math.AT, math.AG, and math.CT
Abstract: A general method of producing correspondences and spectral categories out of symmetric ring objects in general categories is given. As an application, stable homotopy theory of spectra $SH$ is recovered from modules over a commutative symmetric ring spectrum defined in terms of framed correspondences over an algebraically closed field. Another application recovers stable motivic homotopy theory $SH(k)$ from spectral modules over associated spectral categories.