标题： 基于伴随存在的可推导性准则 显示英文标题

标题： A derivability criterion based on the existence of adjunctions

摘要： 在本文中，我们引入了一种基于伴随关系存在的函子可导性准则，而不是基于分解的存在性。 它构成了Quillen-Maltsiniotis导出伴随定理的逆定理。 我们展示了我们可导性准则的两个结果。 一方面，我们证明了对应于Grothendieck导出者和Quillen模型范畴的同伦余极限的两个概念是等价的。 另一方面，我们推导出B. Toen为导出Morita理论构造的内部同态确实是微分分次范畴的内部同态的右导出函子。 显示英文摘要

摘要： In this paper we introduce a derivability criterion of functors based on the existence of adjunctions rather than on the existence of resolutions. It constitutes a converse of Quillen-Maltsiniotis Derived Adjunction Theorem. We present two consequences of our derivability criterion. On the one hand, we prove that the two notions for homotopy colimits corresponding to Grothendieck derivators and Quillen model categories are equivalent. On the other hand, we deduce that the internal hom for derived Morita theory constructed by B. Toen is indeed the right derived functor of the internal hom of dg-categories.