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Bibliography
André, M.A.: L'homotopie des groupes abéliens localement compacts. Comm. Math. Helv.38, 1–5 (1963).
Araki, S.: Cohomology modulo 2 of the compact exceptional groupsE 6 andE 7. J. Math. Osaka City Univ.12, 43–65 (1961).
—: Differential Hopf algebras and the cohomology modulo 3 of the compact exceptional groupsE 7 andE 8. Ann. of Math.73, 404–436 (1961).
Borel, A.: Sur la cohomologie des espaces fibrés principaux et des espaces homogènes de groupes de Lie compacts. Ann. of Math.57, 115–207 (1953).
—: Sur l'homologie et la cohomologie des groupes de Lie compacts connexes. Amer. J. Math.76, 273–342 (1954).
—: Sousgroupes commutatifs et torsion des groupes de Lie compacts connexes. Tohoku Math. J. (2)13, 216–240 (1961).
Cartan, E.: La théorie des groupes finis et continus et l'Analysis Situs. Mem. Sc. Math fasc. 42, Paris: Gauthier-Villars 1930.
Chevalley, C., andS. Eilenberg: Cohomology theory of Lie groups and Lie algebras. Trans. Amer. Math. Soc.63, 85–124 (1948).
Enochs, E.: Homotopy groups of compact abelian groups. Proc. Amer. Math. Soc.15, 878–881 (1964).
Hochschild, G., andJ.P. Serre: Cohomology of Lie algebras. Ann. of Math.57, 591–603 (1953).
Hochschild, G., andG.D. Mostow: Cohomology of Lie groups. Ill. J. Math.6, 367–401 (1962).
Hofmann, K.H.: Homogeneous locally compact groups with compact boundary. Trans. Amer. Math. Soc.106, 52–63 (1963).
Hofmann, K.H.: Introduction to the theory of compact groups I. Tulane University Lecture Notes. Dept. Math. Tulane Univ. 1967.
—, andP.S. Mostert: Elements of compact semigroups. Columbus, Ohio: Charles E. Merrill 1966.
Hu, S.-T.: Cohomology rings of compact connected groups and their homogeneous spaces. Ann. of Math.55, 391–419 (1952).
—: Cohomology theory in topological groups. Mich. Math. J.1, 11–59 (1952).
MacLane, S.: Categorical algebra. Bull. Amer. Math. Soc.71, 40–106 (1965).
Milnor, J.W., andJ.C. Moore: On the structure of Hopf algebras. Ann. of Math.81, 211–264 (1965).
Mitchell, B.: Theory of categories. New York: Academic Press 1965.
Poénaru, V.: Sur la cohomologie des cochaînes singulières invariants sur un groupe topologique compact et connexe. Fund. Math.50, 1–12 (1961/62).
Spanier, E.H.: Algebraic topology. New York: McGraw-Hill 1966.
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This research was partially supported by National Science Foundation Grant GP 6219.
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Hofmann, K.H. Categories with convergence, exponential functors, and the cohomology of compact abelian groups. Math Z 104, 106–140 (1968). https://doi.org/10.1007/BF01109874
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DOI: https://doi.org/10.1007/BF01109874