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Third Mac Lane cohomology

  • HANS–JOACHIM BAUES (a1), MAMUKA JIBLADZE (a2) and TEIMURAZ PIRASHVILI (a3)
Abstract
Abstract

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.

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[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.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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