相关论文: On the straightening of every functor

We initiate the study of derived functors in the setting of extriangulated categories. By using coends, we adapt Yoneda's theory of higher extensions to this framework. We show that, when there are enough projectives or enough injectives,…

We characterise proper morphisms of $\infty$-topoi in terms of a relativised notion of compactness: we show that a geometric morphism of $\infty$-topoi is proper if and only if it commutes with colimits indexed by filtered internal…

We prove that given $\mathcal{C}$ a presentably symmetric monoidal $\infty$-category, and any essentially small $\infty$-operad $\mathcal{O}$, the $\infty$-category of $\mathcal{O}$-algebras in $\mathcal{C}$ is enriched, tensored and…

Let $X \hookrightarrow \overline{X}$ be an open immersion of smooth varieties over a field of characteristic $p>0$ such that the complement is a simple normal crossing divisor and let $\overline{Z} \subseteq Z \subseteq \overline{X}$ be…

Coherence theorems are fundamental to how we think about monoidal categories and their generalizations. In this paper we revisit Mac Lane's original proof of coherence for monoidal categories using the Grothendieck construction. This…

This paper considers the possible underlying multicategories for a symmetric monoidal category, and shows that, up to canonical and coherent isomorphism, there really is only one. As a result, there is a well-defined forgetful functor from…

In this paper we continue the study of triangular matrix categories $\mathbf{\Lambda}=\left[ \begin{smallmatrix} \mathcal{T} & 0 \\ M & \mathcal{U} \end{smallmatrix}\right]$ initiated in [21]. First, given an additive category $\mathcal{C}$…

The goal of this paper is to associate functorially to every symmetric monoidal additive category $\mathbf{A}$ with a strict $G$-action a lax symmetric monoidal functor $\mathbf{V}_{\mathbf{A}}^{G}:G\mathbf{BornCoarse}\to…

We show that differential calculus (in its usual form, or in the general form of topological differential calculus) can be fully imdedded into a functor category (functors from a small category of anchord tangent algebras to anchored sets).…

Let C be a triangulated category with a Serre functor S and X a non-zero contravariantly finite rigid subcategory of C. Then X is cluster tilting if and only if the quotient category C/X is abelian and S(X)=X[2]. As an application, this…

Let $\mathcal{A}$ be a essentially small abelian category and $\mathcal{C}$ be a Serre subcategory of $\mathcal{A}$. Consider the quotient functor $q:\mathcal{A}\rightarrow \mathcal{A}/\mathcal{C}$. For an object $A\in \mathcal{A}$ and a…

In this paper the notion of $\infty$-open-multicommutativity of functors in the category of compact Hausdorff spaces is considered. This property is a generalization of the open-multicommutativity on the case of infinite diagrams. It is…

This paper gives a uniform-theoretic refinement of classical homotopy theory. Both cubical sets (with connections) and uniform spaces admit classes of weak equivalences, special cases of classical weak equivalences, appropriate for the…

Given symmetric monoidal infinity-categories C and D, subject to mild hypotheses on D, we define an infinity-categorical analog of the Day convolution symmetric monoidal structure on the functor category Fun(C, D). An E_infinity monoid for…

For a category $\mathbb{C}$, a small category $\mathbb{I}$, and a pre-cover relation $\sqsubset$ on $\mathbb C$ we prove, under certain completeness assumptions on $\mathbb C$, that a morphism $g: B\to C$ in the functor category $\mathbb…

We suggest two approaches to a definition of unitarity for pseudonatural transformations between unitary pseudofunctors on pivotal dagger 2-categories. The first is to require that the 2-morphism components of the transformation be unitary.…

We prove that if two homomorphisms from O_{\infty} to a purely infinite simple C*-algebra have the same class in KK-theory, and if either both are unital or both are nonunital, then they are approximately unitarily equivalent. It follows…

We define and study cartesian and cocartesian fibrations between categories internal to an $\infty$-topos and prove a straightening equivalence in this context.

We give the definitions of model bicategory and $q$-homotopy, which are natural generalizations of the notions of model category and homotopy to the context of bicategories. For any model bicategory $\mathcal{C}$, denote by…

We investigate $\mathrm{LMod}_{R}(\mathcal{V})$-enriched $\infty$-categories, where $R$ is an $\mathbb{E}_2$-ring in a presentable $\mathbb{E}_2$-monoidal $\infty$-category $\mathcal{V}$, using $\mathcal{V}$-enriched $\infty$-category…