Calculus from comonads

Abstract: (Joint work with Brenda Johnson.) The many theories of "calculus" introduced in algebraic topology over the past couple of decades--e.g., Goodwillie's calculus of homotopy functors, the Goodwillie-Weiss manifold calculus, the orthogonal calculus, and the Johnson-McCarthy cotriple calculus--all have a similar flavor, though the objects studied and exact methods applied are not the same. We have constructed a relatively simple category-theoretic machine for producing towers of functors from a small category into a simplicial model category, determined conditions under which such tower-building machines constitute a calculus, and showed that this framework encompasses certain well known calculi, as well as providing new classes of examples. The cogs and gears of our machine are cubical diagrams of reflective subcategories and the comonads they naturally give rise to.

In this talk, I will assume no familiarity with comonads and only basic knowledge of simplicial model categories.

algebraic topology

Audience: researchers in the topic

Online algebraic topology seminar

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