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.
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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 strecksrbut the actual question seems to be whether you need to learn 1-category theory before some of the more modern theories.
ACC is good too, but also rather idiosyncratic in different ways than Mac Lane.
Sigma Series in Pure Mathematics — Volume 1. Categories and Structures F. Is Mac Lane still the best place to learn category theory? I wish it was the one I’d teory from. The implicit assumption is that the student has a budget of zero dollars. Isomorphisms and equivalences of categories.
Or has this subject become so separate nowadays that we are no longer counting it into category theory? If so, via what route? Student has no knowledge of 1-category theory or simplicial sets and wishes to get the flavor of infinity-category theory, without getting bogged down by technical details, in as short a time as can be reasonably expected.
It is really an excellent exposition with some nice perspectives on the concepts, supported by plenty of examples.
Category Theory by Horst Herrlich, George E. Strecker
Note that it is provided in German only. Hope this may help. Each chapter contains numerous exercises for further study and control.
The idea of a derived generation makes my cringe a little So the next generation will be, so to speak, natively derived.
I would start from “Sets for mathematics”, and then going to MacLane. I third what Mike wrote: Category theory for working mathematicians I’ve already said a lot about this S. Post as a guest Name. Eugenia Cheng’s notes on category theory was tremendously useful.
As a corollary, the best place to learn category theory is in a good algebra textbook together with a good topology textbook and, for optimal rsults, a good algebraic topology textbook.
With that being said, elaborating and expounding upon janed0e’s suggestion, what follows are two study plans according to the prior knowledge of the student. The first chapter of Leinster’s Higher operads, higher categories gives a nice and quick introduction to category theory.
The more advanced book ” Abstract and Concrete Categories “, which the authors of this book wrote together with Jiri Adamek, is also available from Heldermann Verlag as a free electronic publication. You may find this helpful: Lurie’s “Higher Topos Theory” http: My opinion is that one should learn most of category theory before one actually learns category theory, in the form of examples.
Sets for mathematicians is pretty. Handbook of Categorical Algebra 2: Of course, there is no canonical way to approach learning higher category theory, so adjust the readings as needed.
New categories from old. My full review can be found here. Anyway there isn’t a best book to learn basic category theory, any person could find a book better than another one, so I suggest you to take a look a some of these books, then choose which one is the best for you: Monomorphisms, epimorphisms, and bimorphisms. Constant morphisms, zero morphisms, and pointed categories. Epi, extremal mono and extremal epi, mono categories.
The n-category cafe, to keep you going. I’m a fan of Kashiwara and Schapira’s “Categories and sheaves” Horst Herrlich was professor of mathematics at the University of Bremen, Germany. The fact that the book appears in a 3rd edition proves that the authors achieved their goals.
It’s a remarkable book and I think it’s going to replace MacLane very quickly once it’s known to most experts. Best paper to get a feel for Category Theory is “When is one thing equal to some other thing” by Barry Mazur.
Sign up or log in Sign up using Google. 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. I recommend for a first reading on category theory: Horst Herrlich, George E.
Repeating what Giorgio Mossa wrote, 0 has an abundant number of examples from topology, algebra, and theoretical computer science.
Characterization and generation of E-reflective subcategories. Best of all, it’s much cheaper then MacLane! Rarely have I had a question about categories which it has been unable to answer. Normal and exact categories. Inverse and direct limits.
Basic Category Theory F.