現代数学の系譜11 ガロア理論を読む15 [転載禁止]©5ch.io
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0304現代数学の系譜11 ガロア理論を読む
2015/09/06(日) 15:46:16.91ID:+jlmffBhhttps://en.wikipedia.org/wiki/Saunders_Mac_Lane
Saunders Mac Lane (4 August 1909 ? 14 April 2005) was an American mathematician who co-founded category theory with Samuel Eilenberg.
Contributions
After a thesis in mathematical logic, his early work was in field theory and valuation theory. He wrote on valuation rings and Witt vectors, and separability in infinite field extensions.
He started writing on group extensions in 1942, and in 1943 began his research on what are now called Eilenberg?MacLane spaces K(G,n), having a single non-trivial homotopy group G in dimension n.
This work opened the way to group cohomology in general.
After introducing, via the Eilenberg?Steenrod axioms, the abstract approach to homology theory, he and Eilenberg originated category theory in 1945. He is especially known for his work on coherence theorems.
A recurring feature of category theory, abstract algebra, and of some other mathematics as well, is the use of diagrams, consisting of arrows (morphisms) linking objects, such as products and coproducts.
According to McLarty (2005), this diagrammatic approach to contemporary mathematics largely stems from Mac Lane (1948).
Mac Lane also coined the term Yoneda lemma for a lemma which is an essential background to many central concepts of category theory and which was discovered by Nobuo Yoneda.[7]
つづく
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