کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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6414791 | 1630516 | 2014 | 38 صفحه PDF | دانلود رایگان |
In this article we establish the foundations of the Morita homotopy theory of Câ-categories. Concretely, we construct a cofibrantly generated simplicial symmetric monoidal Quillen model structure (denoted by MMor) on the category C1âcat of small unital Câ-categories. The weak equivalences are the Morita equivalences and the cofibrations are the â-functors which are injective on objects. As an application, we obtain an elegant description of Brown-Green-Rieffelʼs Picard group in the associated homotopy category Ho(MMor). We then prove that Ho(MMor) is semi-additive. By group completing the induced abelian monoid structure at each Hom-set we obtain an additive category Ho(MMor)â1 and a composite functor C1âcatâHo(MMor)âHo(MMor)â1 which is characterized by two simple properties: inversion of Morita equivalences and preservation of all finite products. Finally, we prove that the classical Grothendieck group functor becomes co-represented in Ho(MMor)â1 by the tensor unit object.
Journal: Journal of Algebra - Volume 398, 15 January 2014, Pages 162-199