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Representability and autoequivalence groups
Mathematical Proceedings of the Cambridge Philosophical Society ( IF 0.6 ) Pub Date : 2021-02-08 , DOI: 10.1017/s0305004121000086
XIAO–WU CHEN

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:

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。
更新日期:2021-02-08
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