Skip to main content
    • Aa
    • Aa

Third Mac Lane cohomology


MacLane cohomology is an algebraic version of the topological Hochschild cohomology. Based on the computation of the third author (see Appendix) we obtain an interpretation of the third Mac Lane cohomology of rings using certain kind of crossed extensions of rings in the quadratic world. Actually we obtain two such interpretations corresponding to the two monoidal structures on the category of square groups.

Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[4] H.-J. Baues and W. Dreckmann . The cohomology of homotopy categories and the general linear group. K-theory 3 (1989), 307338.

[5] H.-J. Baues M. Hartl and T. Pirashvili . Quadratic categories and square rings. J. Pure Appl. Algebra 122 (1997), 140.

[6] H.-J. Baues and N. Iwase . Square rings associated to elements in homotopy groups of spheres. Contemp. Math. 274 (2001), 5778.

[8] H.-J. Baues and E. C. Minian . Crossed extensions of algebras and Hochschild cohomology. Homology, Homotopy Appl. 4 (2002), 6382.

[9] H.-J. Baues and T. Pirashvili . Quadratic endofunctors of the category of groups. Adv. Math. 141 (1999), 167206.

[10] H.-J. Baues and T. Pirashvili . A universal coefficient theorem for quadratic functors. J. Pure Appl. Algebra 148 (2000), 115.

[12] H.-J. Baues and G. Wirsching . Cohomology of small categories. J. Pure Appl. Algebra 38 (1985), 187211.

[13] S. Eilenberg and S. Mac Lane . On the groups H(π,n), II. Ann. Math. 60 (1954), 49139.

[14] G. Hochschild On the cohomology groups of an associative algebra. Ann. of Math. (2) 46 (1945), 5867.

[17] M. Jibladze and T. Pirashvili . Cohomology of algebraic theories. J. Algebra 137 (1991), 253296.

[18] A. Lazarev Homotopy theory of A∞ ring spectra and applications to MU-modules. K-theory 24 (2001), 243281.

[19] J.-L. Loday . Spaces with finite many nontrivial homotopy groups. J. Pure Appl. Algebra 24 (1982), 179202.

[23] S. Mac Lane and J. H. C. Whitehead . On the 3-type of a complex. Proc. Nat. Acad. Sci. USA 36 (1950), 4148.

[27] T. Pirashvili . Polynomial approximation of and groups in functor categories. Comm. Algebra 21 (1993), 17051719.

[28] T. Pirashvili . On the topological Hochschild homology of ℤ/pk. Comm. Algebra 23 (1995), no. 4, 15451549.

[30] T. Pirashvili and F. Waldhausen . Mac Lane homology and topological Hochschild homology. J. Pure Appl. Algebra 82 (1992), 8198.

[33] S. Schwede Stable homotopy of algebraic theories. Topology 40 (2001), 141.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Full text views

Total number of HTML views: 0
Total number of PDF views: 6 *
Loading metrics...

Abstract views

Total abstract views: 38 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 20th August 2017. This data will be updated every 24 hours.