Category theory: an introduction. Front Cover. Horst Herrlich, George E. Strecker. Allyn and Bacon, – Mathematics – pages. Category Theory: An Introduction. Front Cover. Horst Herrlich, George E. Strecker . Heldermann, – Categories (Mathematics). – pages. Category Theory has 1 rating and 0 reviews: Published by Allyn and Bacon, pages, Hardcover.
As far as a textbook for 1-category theory goes, I’m fond of Awodey’s book.
Category Theory: An Introduction – Horst Herrlich, George E. Strecker – Google Books
As Mike Shulman noted, 0 is rather idiosyncratic. Abstract and Etrecker Categories: Generating, extremal mono and extremal generating, mono factorizations. ACC is good too, but also rather idiosyncratic in different ways than Mac Lane. There’s a bit of truth to that, Mariano, although “most of category theory” is an exaggeration, and it doesn’t address the OP’s concern. She posted her evolving notes at her website each time and the first time I saw a rough draft, I knew she was writing something special.
Category theory Peculiar because it has very low prerequisites and it’s rich of examples too.
Best paper to get a feel for Category Theory is “When is one thing equal to some other thing” by Barry Mazur. Email Required, but never shown. Handbook of Categorical Algebra 3: It’s comprehensive, incredibly clear and amazingly rich in examples, including many you’ve probably never considered.
The paper can be obtained at I doubt that someone could learn higher category theory and more in general higher dimensional algebra without first studying a little of category ztrecker, mostly because the definition given in such context use a lot of category theoretic machinery. Rarely have I had a question about categories which it has been unable to answer.
John Baez, in his not so weekly blog, inspiring. I wish it was the one I’d learned from. The implicit assumption is that the student has a budget of zero dollars. Or has this subject become so separate nowadays that we are no longer counting it into category theory? The idea of a derived generation makes my cringe a little Higher Topos Theory http: Sections, retractions, and isomorphisms. Epi, extremal mono and extremal epi, mono categories. MacLane’s “Category theory for working mathematicians” may be a categorry outdated but I think it is still one of the most complete book of basic category theory second just to Borceux’s books.
An elementary illustrated introduction to simplicial sets 2 J. Eventually, Mac Lane began to make sense, as did Borceux; but oh, ever so slowly. Is Mac Lane still the best place to learn category theory?
I found the Catsters on YouTube divinely useful. You have to hunker down and really learn category theory. The title question looks like it’s asking the best book to learn category theory from which anyway may be impossible to answer; different books address different needsbut the actual question seems to be whether you need to learn 1-category theory before some of the more modern theories. Yeah, I’d say they’re separate enough and you’re better off reading Riehl and then moving on to EGNO’s Tensor Categories if you’re wanting to know more about monoidal categories.
You may find this helpful: If you’re interested in category theory, this is the book you want to learn from.
I found “On the Classification of TQFTs” more readable, because Lurie doesn’t there try to give all detailed definitions, just outline a theody. Eugenia Cheng’s notes on category theory was tremendously useful.
Student has knowledge of 1-category theory but not simplicial sets and wishes to get an in depth experience of infinity-category theory, allowing an ‘ample’ amount of time. My full review can be found here.
Best of all, it’s much cheaper then MacLane! Sets for mathematicians is pretty.
Is Mac Lane still the best place to start? A lot of thanks to Konrad S. Let’s please stay on topic here.
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