The famous “algebraic Mayer–Vietoris theorem” is usually stated for complexes over an Abelian category. In the present paper, this theorem is generalized for complexes over a preabelian category. The proofs are based on the technique and results of the relative homological algebra developed by the author earlier.
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References
P. Selick, Introduction to Homotopy Theory, AMS, Fields Inst. Monographs, 9 (1997).
A. I. Generalov, “Relative homological algebra in preabelian categories, I. Derived categories,” Algebra Analiz, 4, No. 1, 98–119 (1992).
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A. I. Generalov, “Ker-Coker-sequence for preabelian category,” in: Abelian Groups and Modules, Tomsk, No. 11–12 (1994), pp. 78–89.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 492, 2021, pp. 61–68.
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Generalov, A.I. Algebraic Mayer–Vietoris Sequence. J Math Sci 264, 39–43 (2022). https://doi.org/10.1007/s10958-022-05976-9
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DOI: https://doi.org/10.1007/s10958-022-05976-9