Difference between revisions of "Category theory"
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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]]. | 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 | + | Category theory is considered very powerful by some mathematicians. But is considered unnecessarily abstract by other mathematicians, so much so that they jokingly refer to it as "[[abstract nonsense]]". |
[[category:mathematics]] | [[category:mathematics]] | ||
Revision as of 19:49, 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 unnecessarily abstract by other mathematicians, so much so that they jokingly refer to it as "abstract nonsense".