Abstract
We give a characterization of the extriangulated categories which admit the structure of a triangulated category. We show that these are the extriangulated categories where for every object X in the extriangulated category, the morphism 0 → X is a deflation and the morphism X → 0 is an inflation. We thereby give an explicit proof to the statement that for a Frobenius extriangulated category ∐ where proj ( ∐ ) = 0 , its stable category is triangulated.
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