Abstract

For every positively graded algebra A, we show that its categories of linear complexes of projectives and almost injectives (see definition below) are both naturally equivalent to the category of graded modules over the quadratic dual algebra A^!. In case A = Λ is a graded factor of a path algebra with Yoneda algebra Γ, we show that the category Lc_Γ of linear complexes of finitely generated right projectives over Γ is dual to the category of locally finite graded left modules over the quadratic algebra Λ associated to Λ. When Λ is Koszul and Γ is graded right coherent, we also prove that the suspended category gr_Λ has a (triangulated) stabilization S(gr_Λ) which is triangle-equivalent to the bounded derived category of the ‘category of tails’ fpgr_Γ ∕ L_Γ.

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