A **triangulated category** is called **algebraic** (in the sense of B. Keller) if it is equivalent to the stable category of a Quillen exact category of a Frobenius category (a Quillen exact category is Frobenius if it has enough injectives and enough projectives and the two classes coincide).

- B. Keller,
*On differential graded categories*, In: Proc. ICM, Madrid, 2006. vol. II, pp. 151–190, Eur. Math. Soc., Zürich (2006) pdf - Stefan Schwede,
*Algebraic versus topological triangulated categories*, in Triangulated categories, 389–407, London Mathematical Society Lecture Notes**375**, - Fernando Muro, Stefan Schwede, Neil Strickland,
*Triangulated categories without models*, Invent. math.**170**, 231–241 (2007) doi, pdf

Every algebraic triangulated category which is well generated in the sense of Amnon Neeman is triangle equivalent to a localization of the derived category of a small pretriangulated dg-category by a localizing subcategory generated by a set of objects:

- M. Porta,
*The Popescu-Gabriel theorem for triangulated categories*, Adv. Math.**225**(2010) 1669-1715 doi

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