Skip to main content
SpringerLink
Log in

The Lambek Invariants of Commutative Squares in a Homological Category

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

We consider the Lambek invariants in the context of semiexact and homological categories in the sense of Grandis. We generalize the Lambek isomorphism theorem to semiexact and homological categories.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. Lambek, “Goursat’s theorem and homological algebra,” Can. Math. Bull. 7, 597–608 (1964).

    Article  MathSciNet  Google Scholar 

  2. J. B. Leicht, “Axiomatic proof of J. Lambek’s homological theorem,” Can. Math. Bull. 7 609–613 (1964).

    Article  MathSciNet  Google Scholar 

  3. Y. Nomura, “An exact sequence generalizing a theorem of Lambek,” Arch. Math., 22, 467–478 (1971).

    Article  MathSciNet  Google Scholar 

  4. Ya. A. Kopylov, “On the Lambek invariants Ker and Im of commutative squares in a quasi-Abelian category,” Sci. Ser. A, Math. Sci. 11, 57–67 (2005).

  5. M. Grandis, “On the categorical foundations of homological and homotopical algebra,” Cah. Topologie Géom. Différ. Catég. 33, No. 2, 135–175 (1992).

    MathSciNet  Google Scholar 

  6. M. Grandis, Homological Algebra in Strongly Non-Abelian Settings, World Scientific, Hackensack, NJ (2013).

    Book  Google Scholar 

  7. A. Connes and C. Consani, “Homological algebra in characteristic one,” High. Struct. 3, No. 1, 155–247 (2019).

    Article  MathSciNet  Google Scholar 

  8. T. Fritz, “Non-Abelian and ε-curved homological algebra with arrow categories,” J. Pure Appl. Algebra 227, No. 6, Article ID 107314 (2023).

  9. Ya. A. Kopylov and S.-A. Wegner, “On the notion of a semi-Abelian category in the sense of Palamodov,” Appl. Categ. Struct. 20, No. 5, 531–541 (2012).

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Sobolev Institute of Mathematics SB RAS, 4, Akad. Koptyuga pr., Novosibirsk, 630090, Russia

    Ya.A. Kopylov

  2. Novosibirsk State University, 1, Pirogova St., Novosibirsk, 630090, Russia

    V.È. Leshkov

Authors
  1. Ya.A. Kopylov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V.È. Leshkov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ya.A. Kopylov.

Additional information

Translated from Problemy Matematicheskogo Analiza 126, 2024, pp. 5-15.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kopylov, Y., Leshkov, V. The Lambek Invariants of Commutative Squares in a Homological Category. J Math Sci 279, 455–467 (2024). https://doi.org/10.1007/s10958-024-07024-0

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-024-07024-0

Search

Navigation