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Tim Hosgood (Mar 19 2021 at 20:02):Friday, 21:00 UTC
Tim Hosgood (Mar 19 2021 at 20:03):Abstract:
Polynomial monads on slices of the infinity-category of spaces can be described as cartesian monads whose underlying endofunctor is accessible and preserves weakly contractible limits. Such "polynomial" monads can be considered in more general settings, and I will explain how polynomial monads on presheaf infinity-categories are closely related (through an infinity-categorical version of Weber's Nerve Theorem) to monads describing homotopy-coherent algebraic structures defined in terms of "Segal conditions". This is joint work with Hongyi Chu.