Displaying similar documents to “Gabriel filters in Grothendieck categories.”

Idempotent completion of pretriangulated categories

Jichun Liu, Longgang Sun (2014)

Czechoslovak Mathematical Journal

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A pretriangulated category is an additive category with left and right triangulations such that these two triangulations are compatible. In this paper, we first show that the idempotent completion of a left triangulated category admits a unique structure of left triangulated category and dually this is true for a right triangulated category. We then prove that the idempotent completion of a pretriangulated category has a natural structure of pretriangulated category. As an application,...