Mathieu, Martin; Rosbotham, Michael Schanuel’s lemma for exact categories. (English) Zbl 1491.18003 Complex Anal. Oper. Theory 16, No. 5, Paper No. 76, 12 p. (2022). Summary: We prove an injective version of Schanuel’s lemma from homological algebra in the setting of exact categories. MSC: 18A20 Epimorphisms, monomorphisms, special classes of morphisms, null morphisms 18G20 Homological dimension (category-theoretic aspects) 18G50 Nonabelian homological algebra (category-theoretic aspects) Keywords:cohomological dimension; injective object; exact structures PDFBibTeX XMLCite \textit{M. Mathieu} and \textit{M. Rosbotham}, Complex Anal. Oper. Theory 16, No. 5, Paper No. 76, 12 p. (2022; Zbl 1491.18003) Full Text: DOI arXiv References: [1] Ara, P., Mathieu, M.: Sheaf cohomology for \(C^*\)-algebras. Memoir in preparation · Zbl 1213.46044 [2] Bühler, T., Exact categories, Expo. Math., 28, 1, 1-69 (2010) · Zbl 1192.18007 · doi:10.1016/j.exmath.2009.04.004 [3] Bühler, T.: On the algebraic foundations of bounded cohomology. Mem. Amer. Math. Soc., 214(1006):xxii+97, (2011) · Zbl 1237.18001 [4] Lam, T.Y.: Lectures on modules and rings. Graduate Texts in Mathematics, vol. 189. Springer-Verlag, New York (1999) · Zbl 0911.16001 [5] Mac Lane, S.: Homology. Classics in Mathematics. Springer-Verlag, Berlin, (1995). Reprint of the 1975 edition · Zbl 0818.18001 [6] Mathieu, M., Rosbotham, M.: Exact structures for operator modules. Canad. J. Math., to appear, arXiv:2105.05006 · Zbl 1468.46063 [7] Osborne, M.S.: Basic homological algebra. Graduate Texts in Mathematics, vol. 196. Springer-Verlag, New York (2000) · Zbl 0948.18001 [8] Rosbotham, M.: Cohomological dimension for \(C^*\)-algebras. PhD. Thesis, Queen’s University Belfast, Belfast, (2021) · Zbl 1468.46063 [9] Rotman, J.J.: Notes on homological algebras. Van Nostrand Reinhold Mathematical Studies, No. 26. Van Nostrand Reinhold Co., New York-Toronto-London, (1970) · Zbl 0222.18003 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.