Extriangulated categories, Hovey twin cotorsion pairs and model structures

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Associahedra for finite‐type cluster algebras and minimal relations between g‐vectors (2019, background): “Extriangulated categories, recently introduced in [72], axiomatize extension-closed subcategories of triangulated categories in a (moderately) similar way that Quillen’s exact categories axiomatize extension-closed subcategories of abelian categories.”