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Relative Cohomology of Algebraic Theories

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Abstract

We construct relative abelian categories in the sense of MacLane for models of algebraic systems in (co)complete abelian categories. As an example, we consider an analogue of Hochschild-Mitchell cohomology for the functor of Yoneda embedding.

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References

  1. Adámek, J., Rosický, J., Vitale, E.M.: Algebraic theories. Cambridge University Press, Cambridge (2011)

    MATH  Google Scholar 

  2. Barr, M., Wells, C.H.: Category theory for computer scientists. Reprints in Theory and Applications of Categories (2012)

  3. Bénabou, J.: Structures algèbriques dans les catégories. Cah. Topol. Géom. Différ. Catég. 10, 1–126 (1968)

  4. Blanc, D.: Generalized André-Quillen cohomology. J. Homotopy Relat. Struct. 161-191, 3 (2008)

  5. Cartan, A., Eilenberg, S.: Homological algebra. Princeton University Press, Princeton (1956)

    MATH  Google Scholar 

  6. Chiteş, A., Chiteş, C.: Separable K-linear categories. Cent. Eur. J. Math. 8, 274–281 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  7. Cibils, C., Redondo, M.: Cartan-Leray spectral sequence for Galois coverings of linear categories. J. Algebra 284, 310–325 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  8. Crole, R.L.: Categories for types. Cambridge University Press, Cambridge (1993)

  9. Grothendieck, A.: Sur quelques points d’algèbre homologique. Tohoku. Math. J., II. Ser. 9, 119–221 (1957)

  10. Herscovich, E., Solotar, A.: Hochschild-Mitchell cohomology and Galois extensions. J. Pure Appl. Alg. 209, 37–55 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  11. Jibladze, M., Pirashvili, T.: Cohomology of algebraic theories. J. Algebra 137, 253–296 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  12. Jibladze, M., Pirashvili, T.: Quillen cohomology and Baues-Wirsching cohomology of algebraic theories. Cah. Topol. Géom. Différ. Catég. 47, 163–205 (2006)

    MathSciNet  MATH  Google Scholar 

  13. MacLane, S.: Categories for the working mathematician. Springer, B (1998)

  14. MacLane, S.: Homology. Springer, B (1963)

  15. Mitchell, B.: Rings with several objects. Adv. Math. 6, 1–161 (1971)

    Article  MATH  Google Scholar 

  16. Oberst, U.: Basiserweiterung in der Homologie kleiner Kategorien. Math. Z 100, 36–58 (1967)

    Article  MathSciNet  MATH  Google Scholar 

  17. Schwede, S.: Stable homotopy of algebraic theories. Topology 40, 1–41 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  18. Xu, F.: Hochschild and ordinary cohomology rings of small categories. Adv. Math. 219, 1872–1893 (2008)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Institute for Theoretical Physics, NSC Kharkov Institute of Physics and Technology, Akademicheskaia St. 1, 61108, Kharkov, Ukraine

    Simeon Pol’shin

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  1. Simeon Pol’shin
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Correspondence to Simeon Pol’shin.

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Pol’shin, S. Relative Cohomology of Algebraic Theories. Appl Categor Struct 25, 447–453 (2017). https://doi.org/10.1007/s10485-016-9466-7

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  • DOI: https://doi.org/10.1007/s10485-016-9466-7

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