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Schanuel’s lemma for exact categories. (English) Zbl 1491.18003

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)
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[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
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