Colin McLarty
Encyclopedia
Philosophical logic
Philosophical logic is a term introduced by Bertrand Russell to represent his idea that the workings of natural language and thought can only be adequately represented by an artificial language; essentially it was his formalization program for the natural language...
and the foundations of
Foundations of mathematics
Foundations of mathematics is a term sometimes used for certain fields of mathematics, such as mathematical logic, axiomatic set theory, proof theory, model theory, type theory and recursion theory...
mathematics
Mathematical logic
Mathematical logic is a subfield of mathematics with close connections to foundations of mathematics, theoretical computer science and philosophical logic. The field includes both the mathematical study of logic and the applications of formal logic to other areas of mathematics...
, as well as in the history of science
History of science
The history of science is the study of the historical development of human understandings of the natural world and the domains of the social sciences....
and of mathematics
History of mathematics
The area of study known as the history of mathematics is primarily an investigation into the origin of discoveries in mathematics and, to a lesser extent, an investigation into the mathematical methods and notation of the past....
.
Research
McLarty's Elementary Categories and Elementary Toposes describes category theoryCategory theory
Category theory is an area of study in mathematics that examines in an abstract way the properties of particular mathematical concepts, by formalising them as collections of objects and arrows , where these collections satisfy certain basic conditions...
and topos theory at an elementary level.
He has written papers about Saunders Mac Lane
Saunders Mac Lane
Saunders Mac Lane was an American mathematician who cofounded category theory with Samuel Eilenberg.-Career:...
, one of the founders of category theory
Category theory
Category theory is an area of study in mathematics that examines in an abstract way the properties of particular mathematical concepts, by formalising them as collections of objects and arrows , where these collections satisfy certain basic conditions...
.
He is a member of the Grothendieck Circle, which provides on-line and open access to many writings about the mathematician Alexandre Grothendieck, whose category-theoretic genius revolutionized Banach-space theory
Banach space
In mathematics, Banach spaces is the name for complete normed vector spaces, one of the central objects of study in functional analysis. A complete normed vector space is a vector space V with a norm ||·|| such that every Cauchy sequence in V has a limit in V In mathematics, Banach spaces is the...
and algebraic geometry
Algebraic geometry
Algebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex...
and whose life has fascinated many biographers and mathematical scientists.
McLarty has also written about the German algebraist, Emma Noether, who was a Jewish woman, and her involvement with German political history.
Positions
At Case Western Reserve UniversityCase Western Reserve University
Case Western Reserve University is a private research university located in Cleveland, Ohio, USA...
(CWRU), Colin McLarty is the Truman P. Handy Professor of Philosophy
Philosophy
Philosophy is the study of general and fundamental problems, such as those connected with existence, knowledge, values, reason, mind, and language. Philosophy is distinguished from other ways of addressing such problems by its critical, generally systematic approach and its reliance on rational...
and the Chair of the Philosophy Department.
At CWRU, he is also a professor of mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
.
McLarty is a member of the faculty of the CWRU program in women's
Women's studies
Women's studies, also known as feminist studies, is an interdisciplinary academic field which explores politics, society and history from an intersectional, multicultural women's perspective...
and gender studies
Gender studies
Gender studies is a field of interdisciplinary study which analyses race, ethnicity, sexuality and location.Gender study has many different forms. One view exposed by the philosopher Simone de Beauvoir said: "One is not born a woman, one becomes one"...
.
See also
- "Abstract nonsenseAbstract nonsenseIn mathematics, abstract nonsense, general abstract nonsense, and general nonsense are terms used facetiously by some mathematicians to describe certain kinds of arguments and methods related to category theory. roughly speaking, category theory is the study of the general form of mathematical...
", a (usually ironic) term for category theoryCategory theoryCategory theory is an area of study in mathematics that examines in an abstract way the properties of particular mathematical concepts, by formalising them as collections of objects and arrows , where these collections satisfy certain basic conditions...
and category-theoretic arguments in homological algebraHomological algebraHomological algebra is the branch of mathematics which studies homology in a general algebraic setting. It is a relatively young discipline, whose origins can be traced to investigations in combinatorial topology and abstract algebra at the end of the 19th century, chiefly by Henri Poincaré and... - "Generalized abstract nonsense", an ironic and affectionate term for topos theory
- Other topos theorists (besides Saunders Mac LaneSaunders Mac LaneSaunders Mac Lane was an American mathematician who cofounded category theory with Samuel Eilenberg.-Career:...
):- Martin HylandMartin HylandJohn Martin Elliott Hyland is professor of mathematics at King's College in the University of Cambridge, England where he is currently head of the Department of Pure Mathematics and Mathematical Statistics...
- Peter JohnstonePeter Johnstone (mathematician)Peter Tennant Johnstone is Professor of the Foundations of Mathematics at St. John's College, Cambridge. He invented or developed a broad range of fundamental ideas in topos theory.-Books by Peter Johnstone:. –-External links:...
- William LawvereWilliam LawvereFrancis William Lawvere is a mathematician known for his work in category theory, topos theory and the philosophy of mathematics.-Biography:...
- Martin Hyland
External links
- Personal website of Colin McLarty
- CWRU website of Colin McLarty
- Grothendieck Circle, which lists McLarty as a member. (A collection of mathematical and biographical information, photos, links about Alexander GrothendieckAlexander GrothendieckAlexander Grothendieck is a mathematician and the central figure behind the creation of the modern theory of algebraic geometry. His research program vastly extended the scope of the field, incorporating major elements of commutative algebra, homological algebra, sheaf theory, and category theory...
.)