标题： 一种计算方法在微分分级范畴的同伦理论中的应用 显示英文标题

标题： A Computational Approach to the Homotopy Theory of DG categories

摘要： 我们为半自由微分分次范畴提供了一个具体的圆柱函子。 这使我们能够显式地构造一个同伦余极限函子。 这两个函子是“可计算的”，具体来说，所构造的圆柱函子将有限类型的分次范畴，即具有有限生成态射的半自由分次范畴，映射到一个有限类型的分次范畴。 同伦余极限函子具有类似的性质。 此外，利用圆柱函子，我们给出了半自由分次范畴以及有限类型分次范畴的纤维化范畴，独立于Tabuada的工作。 所有结果同样适用于半自由分次代数。 我们还描述了其在辛拓扑中的应用，并提供了一个简单的例子。 显示英文摘要

摘要： We give a specific cylinder functor for semifree dg categories. This allows us to construct a homotopy colimit functor explicitly. These two functors are "computable", specifically, the constructed cylinder functor sends a dg category of finite type, i.e., a semifree dg category having finitely many generating morphisms, to a dg category of finite type. The homotopy colimit functor has a similar property. Moreover, using the cylinder functor, we give a cofibration category of semifree dg categories and that of dg categories of finite type, independently from the work of Tabuada. All the results similarly work for semifree dg algebras. We also describe an application to symplectic topology and provide a toy example.