Difference between revisions of "Category theory"
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| − | Category theory is a branch of mathematics that studies | + | Category theory is a branch of mathematics that studies and analyzes different types of mapping between sets. |
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| + | A category consists of multiple objects, where an object can be almost anything. For example, an object can be a topological space, for which the category would be all topological spaces. | ||
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| + | Many concepts in mathematics, computer science and mathematical physics can be phrased in the language of categories and morphisms between categories. Categories were first introduced by Samuel Eilenberg and Saunders Mac Lane in 1942 as a tool in the study of [[algebraic topology]]. | ||
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| + | Category theory is considered very powerful by some mathematicians, but is considered overly abstract and unproductive by other mathematicians. | ||
| + | [[category:mathematics]] | ||
Revision as of 03:35, July 2, 2007
Category theory is a branch of mathematics that studies and analyzes different types of mapping between sets.
A category consists of multiple objects, where an object can be almost anything. For example, an object can be a topological space, for which the category would be all topological spaces.
Many concepts in mathematics, computer science and mathematical physics can be phrased in the language of categories and morphisms between categories. Categories were first introduced by Samuel Eilenberg and Saunders Mac Lane in 1942 as a tool in the study of algebraic topology.
Category theory is considered very powerful by some mathematicians, but is considered overly abstract and unproductive by other mathematicians.