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🔖 Introduction to Category Theory | UCLA Continuing Education

Bookmarked Introduction to Category Theory (UCLA Continuing Education)

This course is an introduction to the basic tenets of category theory, as formulated and illustrated through examples drawn from algebra, calculus, geometry, set theory, topology, number theory, and linear algebra.

Category theory, since its development in the 1940s, has assumed an increasingly center-stage role in formalizing mathematics and providing tools to diverse scientific disciplines, most notably computer science. A category is fundamentally a family of mathematical obejcts (e.g., numbers, vector spaces, groups, topological spaces) along with “mappings” (so-called morphisms) between these objects that, in some defined sense, preserve structure. Taking it one step further, one can consider morphisms (so-called functors) between categories. This course is an introduction to the basic tenets of category theory, as formulated and illustrated through examples drawn from algebra, calculus, geometry, set theory, topology, number theory, and linear algebra. Topics to be discussed include: isomorphism; products and coproducts; dual categories; covariant, contravariant, and adjoint functors; abelian and additive categories; and the Yoneda Lemma. The course should appeal to devotees of mathematical reasoning, computer scientists, and those wishing to gain basic insights into a hot area of mathematics.

January 8, 2019 - March 19, 2019
Tuesday 7:00PM - 10:00PM
Location: UCLA
Instructor: Michael Miller
Fee: $453.00

The new catalog is out today and Mike Miller’s Winter class in Category Theory has been officially announced.

Oddly, it wasn’t listed in the published physical catalog, but it’s available online. I hope that those interested in mathematics will register as well as those who are interested in computer science.

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Chris Aldrich

I'm a biomedical and electrical engineer with interests in information theory, complexity, evolution, genetics, signal processing, IndieWeb, theoretical mathematics, and big history. I'm also a talent manager-producer-publisher in the entertainment industry with expertise in representation, distribution, finance, production, content delivery, and new media.

4 thoughts on “🔖 Introduction to Category Theory | UCLA Continuing Education”

  3. Bookmarked Abstract and Concrete Categories: The Joy of Cats by Jirí Adámek, Horst Herrlich, and George E. Strecker (goodreads.com)

    This up-to-date introductory treatment employs the language of category theory to explore the theory of structures. Its unique approach stresses concrete categories, and each categorical notion features several examples that clearly illustrate specific and general cases.
    A systematic view of factorization structures, this volume contains seven chapters. The first five focus on basic theory, and the final two explore more recent research results in the realm of concrete categories, cartesian closed categories, and quasitopoi. Suitable for advanced undergraduate and graduate students, it requires an elementary knowledge of set theory and can be used as a reference as well as a text. Updated by the authors in 2004, it offers a unifying perspective on earlier work and summarizes recent developments.

    Mike Miller has announced in class that he’ll be using Abstract and Concrete Categories: The Joy of Cats as the textbook for his upcoming  Introduction to Category Theory course at UCLA Extension this winter.
    Naturally, he’ll be supplementing it heavily with his own notes.
    A free .pdf copy of the text is also available online.

    Syndicated copies to:


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  4. Acquired Abstract and Concrete Categories: The Joy of Cats by Jirí Adámek, Horst Herrlich, George E. Strecker (Dover Publications)

    This up-to-date introductory treatment employs the language of category theory to explore the theory of structures. Its unique approach stresses concrete categories, and each categorical notion features several examples that clearly illustrate specific and general cases.
    A systematic view of factorization structures, this volume contains seven chapters. The first five focus on basic theory, and the final two explore more recent research results in the realm of concrete categories, cartesian closed categories, and quasitopoi. Suitable for advanced undergraduate and graduate students, it requires an elementary knowledge of set theory and can be used as a reference as well as a text. Updated by the authors in 2004, it offers a unifying perspective on earlier work and summarizes recent developments.

    Purchased for use in Mike Miller’s upcoming class on Category Theory at UCLA beginning in January 2019.

    Syndicated copies to:
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