For a finite dimensional algebra A, the bounded homotopy category of projective A-modules and the bounded derived category of A-modules are dual to each other via certain categories of locally-finite cohomological functors. We prove that the duality gives rise to a 2-categorical duality between certain strict 2-categories involving bounded homotopy categories and bounded derived categories, respectively. We apply the 2-categorical duality to the study of triangle autoequivalence groups.

中文翻译：

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可表示性和自等价组

对于有限维代数一种, 射影的有界同伦范畴一种-modules 和有界派生类别一种-模块通过某些类别的局部有限上同调函子彼此对偶。我们证明了对偶在某些严格的 2 类别之间产生了 2 类别对偶，这些严格的 2 类别分别涉及有界同伦类别和有界派生类别。我们将 2 分类对偶性应用于三角形自等价群的研究。