A model structure on internal categories in simplicial sets

We put a model structure on the category of categories internal to simplicial sets whose weak equivalences are reflected by the nerve functor to bisimplicial sets with Rezk's model structure. This model structure is shown to be Quillen equivalent to Rezk's model structure, thus internal category are another model for $(\infty,1)$-categories.Comment: 39 page

Motivic homological stability for configuration spaces of the line

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Higher Hochschild cohomology of the Lubin-Tate ring spectrum

We give a method for computing factorization homology of \oper{E}_n-algebra using as an input an algebraic version of higher Hochschild homology due to Pirashvili. We then show how to compute higher Hochschild homology and cohomology when the algebra is \'etale in a sense that we make precise. As an application, we compute higher Hochschild cohomology of the Lubin-Tate ring spectrum.Comment: 27 page

Brown categories and bicategories

In a Brown category of cofibrant objects, there is a model for the mapping spaces of the hammock localization in terms of zig-zags of length 2. In this paper we show how to assemble these spaces into a Segal category that models the infinity-categorical localization of the Brown category.Comment: 16 page

Factorization homology and calculus à la Kontsevich Soibelman

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