论文标题
在$（\ infty，2）$的LAX转换，附件和单元上
On lax transformations, adjunctions, and monads in $(\infty,2)$-categories
论文作者
论文摘要
我们使用$（\ infty，2）$类别的灰色张量产品的基本预期性能进行研究（CO）LAX自然变换。使用RIEHL-VERITY和ZAGANIDIS的结果，我们确定了具有（Monadic）右伴随的辅助和单子之间的LAX转换。我们还将其组成的成分是等效的（概括了缺乏的图标”）与观看$（\ infty，2）$ - 类别作为简单的$ \ infty $类别所产生的2个年度性的colax转换。使用此特征，我们通过固定对象上的$ \ infty $ - 单类$ \ infty代数的$ \ infty $ - 类别中的$ \ infty $类别中的$ \ infty $ - 类别。
We use the basic expected properties of the Gray tensor product of $(\infty,2)$-categories to study (co)lax natural transformations. Using results of Riehl-Verity and Zaganidis we identify lax transformations between adjunctions and monads with commutative squares of (monadic) right adjoints. We also identify the colax transformations whose components are equivalences (generalizing the "icons" of Lack) with the 2-morphisms that arise from viewing $(\infty,2)$-categories as simplicial $\infty$-categories. Using this characterization we identify the $\infty$-category of monads on a fixed object and colax morphisms between them with the $\infty$-category of associative algebras in endomorphisms.
