Abstract
We show that methods of functor homology can be applied to monoids.
Similar content being viewed by others
References
Calvo-Cervera, M., Cegarra, A.M., Heredia, B.A.: On the third cohomology group of commutative monoids. arXiv.1406.6835
Grillet, P.A.: Commutative semigroup cohomology. Semigroup Forum 43, 247–252 (1991)
Grillet, P.A.: The commutative cohomology of nilsemigroups. J. Pure Appl. Algebra 82, 233–251 (1992)
Grillet, P.A.: Commutative semigroup cohomology. Commun. Algebra 23, 3573–3587 (1995)
Grillet, P.A.: The commutative cohomology of finite semigroup. J. Pure Appl. Algebra 102, 25–47 (1995)
Grillet, P.A.: Cocycles in commutative semigroup cohomology. Commun. Algebra 25, 3425–3462 (1997)
Grillet, P.A.: The commutative cohomology of two-generator semigroups. Semigroup Forum 60, 4–15 (2000)
Leech, J.: \({\cal {H}}\)-coextensions of monoids. Memoirs A.M.S. 157, 1–66 (1975)
Loday, J.-L.: Opérations sur l’homologie cyclique des algébres commutatives. Invent. Math. 96, 205–230 (1989)
Loday, J.-L.: Cyclic Homology, Grund Math. Wiss, vol. 301, 2nd edn. Springer, Heidelberg (1998)
MacLane, S.: Homology. Classics in Mathematics. Springer, Berlin (1995). x+422 pp.
Pirashvili, T.: Hodge decomposition of higher order Hochschild homology. Ann. Sci. École Norm. Sup. (4) 33(2), 151–179 (2000)
Pirashvili, T.: André-Quillen homology via functor homology. Proc. AMS 131, 1687–1694 (2002)
Pirashvili, T.: Dold-Kan type theorem for \(\Gamma \)-groups. Math. Ann. 318(2), 277–298 (2000)
Pirashvili, T., Richter, B.: Robinson-Whitehouse complex and stable homotopy. Topology 29, 525–530 (2000)
Quillen, D.G.: Homotopical algebra. Lecture Notes in Mathematics No. 43. Springer, Berlin (1967). iv+156 pp.
Quillen, D.G.: On the (co)homology of commutative rings. AMS Proc. Sym. Pure Math. 17, 65–87 (1970)
Acknowledgments
The second author is very grateful to Antonio Cegarra for interesting communication on the subject. The authors would like to thank the referee for his careful reading and many valuable suggestions. Research was partially supported by the GNSF Grant ST08/3-387. The second author acknowledgement the support given by the University of Leicester in granting academic study leave.
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by László Márki.
Rights and permissions
About this article
Cite this article
Kurdiani, R., Pirashvili, T. Functor homology and homology of commutative monoids. Semigroup Forum 92, 102–120 (2016). https://doi.org/10.1007/s00233-014-9683-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00233-014-9683-z