Branches of Mathematics
Category Theory
Also Known As Abstract Nonsense
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Category theory is a general theory of mathematical structures and their relations, providing a unifying language for constructions that recur across different areas of mathematics.
Facts
Central QuestionWhat is common to the structures and constructions that recur across different branches of mathematics, independent of the particular objects involved? 1 Key DebateThe subject was informally nicknamed general abstract nonsense at its own 1942 founding, in Saunders Mac Lane's recollection of introducing categories with Samuel Eilenberg, a self-deprecating name for its high level of abstraction that stuck as an affectionate, non-derogatory term among mathematicians rather than a real objection to the subject's usefulness. 2 Cross-Tradition Connections
Sources
1. Category Theory (Wikipedia)
Wikimedia Foundationlead paragraphQuote, lead paragraph
Category theory is a general theory of mathematical structures and their relations.
2. Abstract Nonsense (Wikipedia)
Wikimedia Foundationlead paragraphQuote, lead paragraph
a subject then called 'general abstract nonsense'
Alexander Grothendieck (Wikipedia)
WikipediaIncludes: Alexander Grothendieck, Lead sectionQuote, Includes: Alexander Grothendieck, Lead section
His research extended the scope of the field and added elements of commutative algebra, homological algebra, sheaf theory, and category theory to its foundations, while his so-called "relative" perspective led to revolutionary advances in many areas of pure mathematics.
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