Category Theory in Context (Aurora: Dover Modern Math Originals)

Muy buen libro para profundizar en teoría de categorías, aunque no lo recomendaría para un primer contacto con la materia (Awodey es un buen comienzo). Si bien la impresión no es de buena calidad (bajo gramaje de las hojas), no se puede pedir más por un precio tan bajo. También es de destacar que la autora haya tenido la gentileza de dejar disponible el pdf gratis para descargar desde su página web.

Recebi hoje 29/04/24. Livro de capa comum, excelente impressão, porém letras são pequenas.

I returned to this book after some time passed and I appreciate it more. First of all, it wasn't all that hard to eventually fill in the gaps and be able to use the book. Second, ChatGPT and other LLMs are now available for interactively filling in gaps, and self-contained introductions seem less important now than they did a few years ago. After getting past my initial difficulties, I can also appreciate that the author's contextualization of the material with quotations, hints, and footnotes and the choice of references is very well considered and useful. This is how I felt initially (original review, 4 stars): I'm using this book for self-study and started out reading and working problems as I went along. It didn't work: the book is too difficult as a first text for this purpose. I do think this is a good book, but it's too advanced for a first introduction. There are some statements in the introduction to the effect that few prerequisites are required if you also have some "mathematical maturity". Don't be fooled: this is code for already knowing category theory, and some essential definitions are missing. I recommend that if you are acquiring category theory by self-study you should start with "Category Theory for the Working Mathematician," because that book does define everything with complete clarity. And don't let the title of that book scare you: it is perfectly sufficient for the beginner. Steve Awodey's book "Category Theory" is another good starting point or second reference. Essentially this is the problem: to understand basic category theory you need an unambiguous interpretations of commutative and non-commutative diagrams, abstract categories ("metacategories"), and concrete categories. Then as each auxiliary definition and tool is built up you need to understand its construction unambiguously and in its full generality. These things are all fairly simple. I'm observing that once people understand all of these things together as a "language" they enjoy the experience so much that they immediately forget how to explain the basic definitions to their readers and want to just write category theory at you. And to some extent that is a positive and promising thing. I'm hoping that once I get my basic grounding in category theory and come back to finish reading this book that the more advanced material is presented well enough that I can understand it. I expect that that will be true based on reviews by more advanced readers.

Es difícil de leer para estudiantes de licenciatura (como yo), pero presenta muchísimos ejemplos y la teoría se expone de manera muy interesante. Varias veces he quedado asombrado por los resultados que aparecen y cómo generalizan conceptos de diferentes ramas de la matemática simultáneamente. Me encanta!

Riehl always exhibits plenty of examples of mathematical phenomena BEFORE giving the categorical concept that subsumes them all. The effect is that category theory is seen as revelatory. In reponse to the usual saying that "there are no theorems in category theory," she also gives lots of categorical theorems, in other branches of math as well as in category theory itself. A fun and elucidating read!