Related papers: Parametrized higher category theory

Univalent homotopy type theory (HoTT) may be seen as a language for the category of $\infty$-groupoids. It is being developed as a new foundation for mathematics and as an internal language for (elementary) higher toposes. We develop the…

Colimits are a fundamental construction in category theory. They provide a way to construct new objects by gluing together existing objects that are related in some way. We introduce a complementary notion of anticolimits, which provide a…

We present an abstract version of Goerss-Hopkins theory in the setting of a prestable $\infty$-category equipped with a suitable periodicity operator. In the case of the $\infty$-category of synthetic spectra, this yields obstructions to…

We prove a generalization of Quillen's Theorem B to strict $\infty$-categories. More generally, we show that under similar hypothesis as for Theorem B, the comma construction for strict $\infty$-categories, that we introduced with…

We show that the stable module $\infty$-category of a finite group $G$ decomposes in three different ways as a limit of the stable module $\infty$-categories of certain subgroups of $G$. Analogously to Dwyer's terminology for homology…

We extend Bourke and Garner's idempotent adjunction between monads and pretheories to the framework of $\infty$-categories and we use this to prove many classical results about monads in the $\infty$-categorical framework. Amongst other…

We present a general approach to construct a class of generalized topological field theories with constraints by means of generalized differential calculus and its application to connection theory. It turns out that not only the ordinary BF…

In a previous paper I gave a presentation for the Quillen higher algebraic K-groups of an exact category in terms of "acyclic binary multicomplexes". In this paper I take that presentation as a definition of the higher K-groups, generalize…

We associate to every $G$-bornological coarse space $X$ and every left-exact $\infty$-category with $G$-action a left-exact infinity-category of equivariant $X$-controlled objects. Postcomposing with algebraic K-theory leads to {new}…

We introduce group corings, and study functors between categories of comodules over group corings, and the relationship to graded modules over graded rings. Galois group corings are defined, and a Structure Theorem for the $G$-comodules…

Given a diagram of rings, one may consider the category of modules over them. We are interested in the homotopy theory of categories of this type: given a suitable diagram of model categories M(s) (as s runs through the diagram), we…

This paper is mainly about an early result that the orbifold stack is globally representable via some $ \infty $-categorical techniques.

Building on work by Fiore-Pronk-Paoli, we construct four model structures on the category of double categories, each modeling one of the following: simplicial spaces, Segal spaces, $(\infty,1)$-categories, and $\infty$-groupoids.…

We explain how the notion of homotopy colimits gives rise to that of mapping spaces, even in categories which are not simplicial. We apply the technique of model approximations and use elementary properties of the category of spaces to be…

For a finite group G, we introduce the complete suboperad $Q_G$ of the categorical G-Barratt-Eccles operad $P_G$. We prove that $P_G$ is not finitely generated, but $Q_G$ is finitely generated and is a genuine $E_\infty$ G-operad (i.e., it…

We introduce the notion of weighted limit in an arbitrary quasi-category, suitably generalizing ordinary limits in a quasi-category, and classical weighted limits in an ordinary category. This is accomplished by generalizing Joyal's…

We generalize a recent result of Clausen: For a number field with integers O, we compute the K-theory of locally compact O-modules. For the rational integers this recovers Clausen's result as a special case. Our method of proof is quite…

Let G be a discrete group. We give methods to compute for a generalized (co-)homology theory its values on the Borel construction (EG x X)/G of a proper G-CW-complex X satisfying certain finiteness conditions. In particular we give formulas…

Suppose that a finite group $G$ admits a Frobenius group of automorphisms FH of coprime order with cyclic kernel F and complement H such that the fixed point subgroup $C_G(H)$ of the complement is nilpotent of class $c$. It is proved that…

We present a version of higher Hochschild homology for spaces equipped with principal bundles for a structure group $G$. As coefficients, we allow $E_\infty$-algebras with $G$-action. For this homology theory, we establish an equivariant…