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Parametrised homotopy theory via symmetric retractive spectra

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HHH - Homotopy harnessing higher structures

I shall explain a new framework for parametrised homotopy theory, based on symmetric spectra objects in retractive spaces. In contrast to previous model categorical frameworks it encompasses a well-behaved symmetric monoidal structure, that models the Day-convolution present in the quasi-categorical set-up. As a small application I will give a simple proof, that K-theory as defined through stable homotopy theory agrees with the original geometric construction (even as highly structured objects), a fact that seems to be missing from the literature so far.

This talk is part of the Isaac Newton Institute Seminar Series series.

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