Vol. 52, No. 2, 1974

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Category theory applied to Pontryagin duality

David W. Roeder

Vol. 52 (1974), No. 2, 519–527

A proof of the Pontryagin duality theorem for locally compact abelian (LCA) groups is given, using category-theoretical ideas and homological methods. The proof is guided by the structure within the category of LCA groups and does not use any deep results except for the Peter-Weyl theorem. The duality is first established for the subcategory of elementary LCA groups (those isomorphic with Ti Zj Rk F, where T is the circle group, Z the integers, R the real numbers, and F a finite abelian group), and through the study of exact sequences, direct limits and projective limits the duality is expanded to larger subcategories until the full duality theorem is reached.

Mathematical Subject Classification 2000
Primary: 22B05
Secondary: 22D35
Received: 22 August 1972
Revised: 26 January 1973
Published: 1 June 1974
David W. Roeder