Attached atoms in Grothendieck categories

Let 𝒜 be a Grothendieck category. In this paper we define attached atoms of nonzero objects of 𝒜 as a dual of the associated atoms of nonzero objects introduced by Kanda [2 Kanda, R. (2012). Classifying Serre subcategories via atom spectrum. Adv. Math. 231(3–4):1572–1588. [Google Scholar]]. If R is a (non)commutative ring, then we show that this new notion can be corresponded to the attached prime ideals of nonzero modules introduced by Macdonald [5 Macdonald, I. G. (1973). Secondary representation of modules over a commutative ring. Sympos. Math. 11:23–43. [Google Scholar]] and Annin [1 Annin, S. (2008). Attached primes over noncommutative rings. J. Pure Appl. Algebra 212:510–521.[Crossref], [Web of Science ®] , [Google Scholar]].