A bivariant Yoneda lemma and (infinity, 2)-categories of correspondences

Abstract: The notion of the *category of correspondences* of a category D with a specified, base change stable, class of morphisms S --- whose objects are those of D and whose morphisms are "spans" in D, one side of which belongs to S --- will be familiar to practitioners of Grothendieck's theory of motives. Perhaps less familiar is the fact that an obvious 2-categorical upgrade of correspondences has a universal property: it is the universal way to attach right adjoints to members of S subject to a base change formula.

I will explain a little about the state of the art on enriched and iterated higher categories and show that they can be used to provide a conceptual (that is, no explicit homotopy- or simplex-chasing) proof of this phenomenon for (infinity, 2)-categories. This enhancement opens the door to direct constructions of bivariant homology theories in motivic homotopy theory and beyond.

algebraic geometrydifferential geometrygeometric topologysymplectic geometry

Audience: researchers in the topic

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