Serre injective sheaves (Q1316918)

For \(k\) a field, \(V\) a finite dimensional vector space over \(k\) and \(T\) the tensor algebra of \(V\), the author studies a factor algebra, \(A\), of \(T\) modulo a one sided ideal. Considering \(\text{gr-}A\), the author factors by a full subcategory determined by colimits of certain bounded objects. The resulting factor category in the case that \(A\) is commutative, is equivalent to the category of quasi coherent sheaves on \(\text{Proj}(A)\) by results of Serre. The author calls this quotient category in the general case the category of Serre sheaves. (The translator uses `Serré' but this is clearly wrong.) The remainder of the paper explores cohomology in this category.