The concept of a perverse schober defined by Kapranov–Schechtman is a categorification of the notion of a perverse sheaf. In their definition, a key ingredient is a certain purity property of perverse sheaves. In this short note, we attempt to describe a real analogue of the above story, as categorification of Legendrian points/knots. The notion turns out to include various notions such as semi-orthogonal decomposition, mutation braiding, spherical functor, $N$-spherical functor, and irregular perverse schober.

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传奇结的分类

Kapranov-Schechtman定义的不正当呼应概念是不正当捆概念的分类。在他们的定义中，关键成分是有害滑轮的一定纯度。在本简短说明中，我们尝试将上述故事的真实相似形式描述为Legendrian点/结的分类。事实证明，该概念包括各种概念，例如半正交分解，突变编织，球形函子，$ N $球形函子和不规则的不规则舒伯尔。