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Category Theory

  As modern algebra developed, mathematicians began to realize that the theorems proved in different branches were often very similar to each other. Category theory is the branch of algebra which studies these common properties of algebraic objects. A category consists of two objects: a class of underlying objects (such as fields, groups or rings) and a class of functions between these objects (such as group homomorphisms—those functions between one group and another which preserve multiplication). The reason that these notions have a great deal of generality about them is because they are designed to reflect the common elements between disparate branches of mathematics. The results that can be obtained by the use of category theory are powerful, because of their generality, but they are also very difficult, precisely because they are so general. SMcL

See also abstraction.Further reading S. Maclane, Categories for the Working Mathematician.



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