相关论文: An equivalence between two models of $\infty$-cate…

In this note we study symmetric monoidal functors from a symmetric monoidal 1-category to a cartesian symmetric monoidal $\infty$-category, which are in addition hypersheaves for a certain topology. We prove a symmetric monoidal version of…

We make Hinich's $\infty$-categorical enriched Yoneda embedding natural. To do so, we exhibit it as the unit of a partial adjunction between the functor taking enriched presheaves and Heine's functor taking a tensored category to an…

We show that the tensor product of $\infty$-categories enriched in a suitable monoidal $\infty$-category preserves colimits in each variable, fixing a mistake in an earlier paper of Gepner and the author. We also prove that essentially…

In the well-known settings of category theory enriched in a monoidal category V, the use of V-enriched functor categories and bifunctors demands that V be equipped with a symmetry, braiding, or duoidal structure. In this paper, we establish…

We advance the foundational study of be Nardin-Shah's $\infty$-category of $G$-operads and their associated $\infty$-categories of algebras. In particular, we construct the underlying $G$-symmetric sequence of a (one color) $G$-operad,…

We define the category of tidy symmetric multicategories. We construct for each tidy symmetric multicategory Q a cartesian monad (E_Q,T_Q) and extend this assignation to a functor. We exhibit a relationship between the slice construction on…

In arXiv:1712.00555, H. Heine shows that given a symmetric monoidal $\infty$-category $\mathcal{V}$ and a weakly $\mathcal{V}$-enriched monad $T$ over an $\infty$-category $\mathcal{C}$, then there is an induced action of $\mathcal{V}$ on…

In this paper we introduce a notion of $\mathbf{O}$-monoidal $\infty$-categories for a finite sequence $\mathbf{O}^{\otimes}$ of $\infty$-operads, which is a generalization of the notion of higher monoidal categories in the setting of…

We provide an $(\infty,n)$-categorical version of the straightening-unstraightening construction, asserting an equivalence between the $(\infty,n)$-category of double $(\infty,n-1)$-right fibrations over an $(\infty,n)$-category…

For a monoidal $\infty$-category $\mathcal{M}$ with colimits, we study colimits of $\mathcal{M}$-functors $\mathcal{A}\to\mathcal{B}$ where $\mathcal{B}$ is left-tensored over $\mathcal{M}$ and $\mathcal{A}$ is an $\mathcal{M}$-enriched…

In this paper, we study conditions for extending Quillen model category properties , between two symmetric monoidal categories, to their associated category of symmetric sequences and of operads. Given a Quillen equivalence $\lambda:…

We show that any functor between $\infty$-categories can be straightened. More precisely, we show that for any $\infty$-category $\mathcal{C}$, there is an equivalence between the $\infty$-category $(\mathrm{Cat}_{\infty})_{/\mathcal{C}}$…

For a braided fusion category $\mathcal{V}$, a $\mathcal{V}$-fusion category is a fusion category $\mathcal{C}$ equipped with a braided monoidal functor $\mathcal{F}:\mathcal{V} \to Z(\mathcal{C})$. Given a fixed $\mathcal{V}$-fusion…

We construct a generalization of the Day convolution tensor product of presheaves that works for certain double $\infty$-categories. Using this construction, we obtain an $\infty$-categorical version of the well-known description of…

We introduce the notion of a monoidal category enriched in a braided monoidal category $\mathcal V$. We set up the basic theory, and prove a classification result in terms of braided oplax monoidal functors to the Drinfeld center of some…

In his book on model categories, Hovey asked whether the 2-category $\mathbf{Mod}$ of model categories admits a "model 2-category structure" whose weak equivalences are the Quillen equivalences. We show that $\mathbf{Mod}$ does not have…

We prove that a lax $\mathbb{E}_{n+1}$-monoidal functor from $\mathcal V$ to $\mathcal W$ induces a lax $\mathbb{E}_n$-monoidal functor from $\mathcal V$-enriched $\infty$-categories to $\mathcal W$-enriched $\infty$-categories in the sense…

We define a functor which takes in an $(\infty,1)$-category and outputs an $(\omega,1)$-category, the natural maximally "strict" version of an $(\infty,1)$-category. We do this by modeling $(\infty,1)$-categories as categories enriched in…

In this paper, we show another proof of the problem by constructing a strict monoidal category M(C) consisting of M-functors and M-morphisms of a category C and we prove C is equivalent to it. The proof is based on a basic character of…

In this paper we unify previous developments on higher operads and multitensors into a single framework in which the interplay between multitensors on a category V, and monads on the category of graphs enriched in V, is taken as…