Plus构造的计算

Plus构造、Plethysm与唯一分解范畴及其在图和Operad-like理论中的应用

Plus constructions, plethysm, and unique factorization categories with applications to graphs and operad-like theories

本文在范畴论框架下推广Baez-Dolan型Plus构造，证明其核心性质，并引入唯一分解范畴，解释operads等结构的幺半群表述存在性，为图论与operad-like理论提供统一视角。

Monoidal envelopes and Grothendieck construction for dendroidal Segal objects

We propose a construction of the monoidal envelope of $\infty$-operads in the model of Segal dendroidal spaces, and use it to define cocartesian fibrations of such. We achieve this by viewing the dendroidal category as a "plus construction" of the category of pointed finite sets, and work in the more general language of algebraic patterns for Segal conditions. Finally, we rephrase Lurie's definition of cartesian structures as exhibiting the categorical fibrations coming from envelopes, and deduce a straightening/unstraightening equivalence for dendroidal spaces.

Plethysm 积、元素构造与 Plus 构造

Plethysm Products, Element and Plus Constructions

本文在双模、相对双模和可因子化双模三个层面构造 plethysm 积幺半结构，建立其与 Grothendieck 元素构造等的统一理论，并证明 plus 构造可实现为与幺半结构相容的元素构造，从而得到元素构造与 plus 构造的交换性。

任意辫子幺半范畴范畴中弱双代数和弱霍普夫代数Tannaka对偶的图解法

Graphical Methods for Tannaka Duality of Weak Bialgebras and Weak Hopf Algebras in Arbitrary Braided Monoidal Categories

Tannaka对偶描述了给定范畴中代数对象和它们的表示之间的关系;一个重要的例子是霍普夫代数和它们的表示范畴;这些都有强的monoidal遗忘“纤维函子”到向量空间范畴。我们同时从两个方面推广了Tannaka对偶理论：第一，用弱霍普夫代数代替霍普夫代数，用可分Frobenius monoidal函子代替强monoidal函子;第二，用任意辫状幺半范畴代替向量空间范畴.为了实现这一目标，我们引入了一个新的图形符号之间的函子幺半范畴，使用字符串图与彩色区域。这种符号不仅扩展了我们对复杂计算给出简单证明的能力，而且使弗罗贝纽斯么半群或可分弗罗贝纽斯么半群函子与定义某些代数结构的公理拓扑之间的某些联系变得清晰。最后，将Tannaka推广到任意基范畴，我们简要地讨论了该构造的函性，因为该基是变化的。

辛费米子的辫状幺半范畴

A braided monoidal category for symplectic fermions

我们描述了一类由对称范畴中的霍普夫代数构造的辫状幺半范畴的例子。该结构的动机是在二维共形域论的计算，并定制包含编织幺半范畴类别发生在伊辛模型的研究，他们的概括Tamabara-Yamagami类别，和类别发生辛费米子。

Enriched Koszul duality for dg categories

It is well-known that the category of small dg categories dgCat, though it is monoidal, does not form a monoidal model category. In this paper we construct a monoidal model structure on the category of pointed curved coalgebras ptdCoa* and show that the Quillen equivalence relating it to dgCat is monoidal. We also show that dgCat is a ptdCoa*-enriched model category. As a consequence, the homotopy category of dgCat is closed monoidal and is equivalent as a closed monoidal category to the homotopy category of ptdCoa*. In particular, this gives a conceptual construction of a derived internal hom…