关于多可消函子的普遍性

有理激发函子的代数模型

An algebraic model for rational excisive functors

本文通过类比谱内函子与equivariant稳定同调论，提出有理激发函子的代数模型，并证明其有理分裂性质。

The Long-Moody construction and polynomial functors

In 1994, Long and Moody gave a construction on representations of braid groups which associates a representation of \mathbf{B}\_{n} with a representation of \mathbf{B}\_{n+1}. In this paper, we prove that this construction is functorial and can be extended: it inspires endofunctors, called Long-Moody functors, between the category of functors from Quillen's bracket construction associated with the braid groupoid to a module category. Then we study the effect of Long-Moody functors on strong polynomial functors: we prove that they increase by one the degree of very strong polynomiality.

Homotopy nilpotent groups and their associated functors

To every homotopy n-nilpotent group, defined in earlier work by Dwyer and the author, we associate an endofunctor of pointed spaces and prove that it is looped and n-excisive. As a tool we prove that $ΩP_n({\rm id})$ commutes with sifted colimits of connected spaces.

Shapely monads and analytic functors

In this paper, we give precise mathematical form to the idea of a structure whose data and axioms are faithfully represented by a graphical calculus; some prominent examples are operads, polycategories, properads, and PROPs. Building on the established presentation of such structures as algebras for monads on presheaf categories, we describe a characteristic property of the associated monads---the shapeliness of the title---which says that "any two operations of the same shape agree". An important part of this work is the study of analytic functors between presheaf categories, which are a comm…

Stable $\infty$-Operads and the multiplicative Yoneda lemma

We construct for every $\infty$-operad $\mathcal{O}^\otimes$ with certain finite limits new $\infty$-operads of spectrum objects and of commutative group objects in $\mathcal{O}$. We show that these are the universal stable resp. additive $\infty$-operads obtained from $\mathcal{O}^\otimes$. We deduce that for a stably (resp. additively) symmetric monoidal $\infty$-category $\mathcal{C}$ the Yoneda embedding factors through the $\infty$-category of exact, contravariant functors from $\mathcal{C}$ to the $\infty$-category of spectra (resp. connective spectra) and admits a certain multiplicative…

2-范畴的普遍性及6- functor形式的构造

Universality of span 2-categories and the construction of 6-functor formalisms

本文研究了2-范畴的普遍性，证明了其与双伴随可变换的对应关系，并扩展到对称单子和松散对称单子情形，为6- functor形式的构造提供了理论基础。