2023/06/14 by Abdolnaser Bahlekeh, Bahlekeh, Abdolnaser, Fahimeh Sadat Fotouhi +5 · 1 citation
Chemistry · Mathematics · #Algebraic structures and combinatorial models #Carbohydrate Chemistry and Synthesis #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2306.08267
openalex publication_date 2023/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let n be a non-negative integer. An exact category \C is said to be an n-Frobenius category, provided that it has enough n-projectives and n-injectives and the n-projectives coincide with the n-injectives. It is proved that any abelian category with non-zero n-projective objects, admits a non-trivial n-Frobenius subcategory. In particular, we explore several examples of n-Frobenius categories. Also, as a far reaching generalization of the stabilization of a Frobenius category, we define and study phantom stable category of an n-Frobenius category \C. Precisely, assume that \p⊆\Extn\C is the subfunctor consisting of all conflations of length n factoring through n-projective objects. A couple (\C\p, T), where \C\p is an additive category and T is a covariant additive functor from \C to \C\p, is a phantom stable category of \C, provided that for any morphism f in \C, T(f)=0, whenever f is an n-\Ext-phantom morphism and T(f) is an isomorphism in \C\p, if f acts as invertible on \Extn/\p, and T has the universal property with respect to these conditions. The main focus of this paper is to show that the phantom stable category of an n-Frobenius category always exists. Some properties of phantom stable categories that reveal the efficiency of these categories are studied.