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A generalization of Grothendieck’s extension Panachées

  • Rakesh R PawarEmail author
Article
  • 27 Downloads

Abstract

We consider an extension problem for exact sequences in an abelian category and provide a criterion under which such a solution, if it exists is unique.

Keywords

Abelian categories Yoneda extensions Baer sums 

Mathematics Subject Classification

18E10 18G15 

Notes

Acknowledgements

The question considered in this paper was asked by Prof. B Kahn and was communicated to the author by Prof. V Srinivas. The author would like to thank Prof. V Srinivas for subsequent discussions and guidance that led to this paper. The author would also like to thank Prof. B Kahn for email communication that led to the formulation of condition (ii) in Theorem 1.1. The author would like to thank the anonymous referee for corrections and valuable suggestions that improved the exposition of the material. The work was completed when the author was a Ph.D. student at TIFR, Mumbai and was supported by the Shyama Prasad Mukherjee Fellowship (File No. SPM-07/858(0139)/2012) funded by CSIR, India.

References

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    Freyd P J, Abelian Categories (1964) (Harper and Row)Google Scholar
  2. 2.
    Grothendieck A, Raynaud M and Rim D S, Groupes de Monodromie en Géométrie Algébrique (SGA 7), Lecture Notes in Mathematics, vol. I (1972) (Springer-Verlag)Google Scholar
  3. 3.
    Stacks Project, http://stacks.math.columbia.edu (2019)
  4. 4.
    Weibel Charles A, An Introduction to Homological Algebra, Cambridge Studies in Advanced Mathematics 38 (1994) (Cambridge University Press)Google Scholar

Copyright information

© Indian Academy of Sciences 2019

Authors and Affiliations

  1. 1.Fakultät für MathematikUniversity of Duisburg-EssenEssenGermany

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