![]() ![]() MacLane in Categories for the Working Mathematician ML98 gives a good. Concentrating on common properties of these structures by stripping away the non-essential aspects of a problem clears the path to new results. A monad M on a category C is a functor: it associates to any object X in C. ![]() For example, in the case of vector spaces as mathematical objects, the structure-preserving mappings are the linear transformations, and one can study the ‘category’ of vector spaces using linear mappings as the morphisms between objects of the category. More specifically, one can look at common properties of mathematical objects such as algebraic structures (groups, fields or rings) or topological spaces by studying structure-preserving mappings - ‘morphisms’ - between such objects. In 1945, he and Sammy Eilenberg introduced the basic ideas of category theory, often described as a language of mathematics that allows the description of transformations from one area of the subject into another by distilling their common properties. Saunders Mac Lane, who died on 14 April, was one of the few mathematicians to create a major new concept that has had a lasting effect on the subject. ![]()
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