🔖 Abstract and Concrete Categories: The Joy of Cats by Jiri Adamek, Horst Herrlich, and George E. Strecker

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.

Black and Tealish Green book cover of Abstract and Concrete Categories: The Joy of Cats

9 thoughts on “🔖 Abstract and Concrete Categories: The Joy of Cats by Jiri Adamek, Horst Herrlich, and George E. Strecker”

  1. 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:

  2. 📖 Read pages i-20 the front matter and Introduction of Abstract and Concrete Categories: The Joy of Cats by Jirí Adámek, Horst Herrlich, George E. Strecker

    Some initial discussion of sets, classes, and conglomerates to keep us out of trouble with some of the potential foundational issues that can be found in set theory.
    Highlights, Quotes, Annotations, & Marginalia

    completions of partially orderedsets and of metric spaces,ˇCech-Stone compactifications of topological spaces, sym-metrizations of relations, abelianizations of groups, Bohr compactifications of topo-logical groups, minimalizations of reachable acceptors, etc.  

    The tough part of category theory is lists of things like this right up front which will tend to scare off almost any reader but those who are working on Ph.D.s in mathematics…
    November 30, 2018 at 09:29PM

    Motivation  

    I really wish more math textbooks had motivation sections like this one does.
    November 30, 2018 at 09:35PM

    Therefore we advise the beginner to skip from here, go directly to§3, and return to this section only when the need arises.  

    They’ve buried the lede here apparently.
    November 30, 2018 at 10:15PM

    Kuratowski definition of an ordered pair  

    I don’t think I’ve ever seen the specific name Kuratowski attached to this.
    November 30, 2018 at 10:31PM

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