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The theory of shadows is an axiomatic, bicategorical framework that generalizes topological Hochschild homology (THH) and satisfies analogous important properties, such as Morita invariance. Using Bermans extension of THH to bicategories, we prove that there is an equivalence between functors out of THH of a bicategory and shadows on that bicategory. As an application we provide a new, conceptual proof that shadows are Morita invariant.
We provide an elementary proof of a bicategorical pasting theorem that does not rely on Powers 2-categorical pasting theorem, the bicategorical coherence theorem, or the local characterization of a biequivalence.
We prove that topological Hochschild homology (THH) arises from a presheaf of circles on a certain combinatorial category, which gives a universal construction of THH for any enriched infinity category. Our results rely crucially on an elementary,
We prove a version of J.P. Mays theorem on the additivity of traces, in symmetric monoidal stable $infty$-categories. Our proof proceeds via a categorification, namely we use the additivity of topological Hochschild homology as an invariant of stable
One way of interpreting a left Kan extension is as taking a kind of partial colimit, whereby one replaces parts of a diagram by their colimits. We make this intuition precise by means of the partial evaluations sitting in the so-called bar constructi
We develop a localisation theory for certain categories, yielding a 3-arrow calculus: Every morphism in the localisation is represented by a diagram of length 3, and two such diagrams represent the same morphism if and only if they can be embedded in