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Categorical introduction to Algebra and Topology Ask Question. Asked 5 years, 6 months ago. Active 9 months ago. Viewed 3k times.
It's a more impressive book after you know the material and you're using it as a reference. For learning, it's a little austere for my taste and I don't think I'm the only one. Try Hungerford. Same material, but a bit more user friendly. Bruno Stonek Bruno Stonek 6, 2 2 gold badges 40 40 silver badges bronze badges.
ISBN 13: 9789027726278
But it does not go much beyond stating the universal properties for products and copoproducts, does it? Adjoint functors, Limits, Yoneda's Lemma and all that are entirely ignored, if I remember the table of contents correctly.
All these things are so beautiful to me, I'd like to see them "in action". The mindset of the book is categorical, and as far as I remember every concept that can be introduced and explained categorically is explained in that way. Some concepts are introduced as needed it is an algebra book, not a category theory book , such as adjoint functors which are introduced to explain the free-forgetful adjunction.
It is already much more than can be said of a lot of algebra books that explain free objects groups, modules Yoneda appears in the exercises, maybe because it doesn't appear all that obviously in a first course in algebra. For example, a lot of the material in a standard introduction to group theory.
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The reality is more like: "We don't really know how it works" and that classical thinking becomes a huge hindrance e. That being said: Many things obviously haven't been worked out yet. Do the adjectives that you characterized the category of groups with give any hint of statements as elementary as the Sylow theorems, for instance?
This is about what first-order logic looks like in categorical language. You want to understand the syntactic bi- category of predicates and functional predicates classes associated to a first-order theory. Second, read sections A1 and A2 in order to understand what a topos hence a "set theory" looks like categorically. The relevant material for understanding the constructions of these categories are the first few chapters of Basic Concepts of Enriched Category Theory It is here, in considering the enriched category theory perspective, where having a good understanding of the category of sets as a well-pointed topos is crucial.
Vladimir Sotirov Vladimir Sotirov 8, 1 1 gold badge 20 20 silver badges 51 51 bronze badges. Ronnie's book is wide ranging and very categorical in its approach. Not everything can be proved jst using category theoretic methods, but motivation for constructions can often be given that way.
Categorical Topology Research Papers - dispthrougpikechild.cf
As a plus the groupoid stuff is great for understanding more algebra. Louis Louis 2, 2 2 gold badges 13 13 silver badges 29 29 bronze badges. It might be a very good book for the algebraically-minded student who is taking a first course on topology or anyone with interest on learning algebraic topology as it covers the basic point-set topology material as well Fortunately, there is an english translation of the book which is split into two parts: Elements of point-set topology and Elements of homotopy theory. EternalBlood EternalBlood 2 2 silver badges 18 18 bronze badges.
Giorgio Mossa Giorgio Mossa Sep 3 '18 at Martin Dowd Martin Dowd 59 3 3 bronze badges. It is not good practice to post answers which consist almost entirely of links to other resourcessuch links can suffer from "link rot," or go to places which are not accessible to everyone e.
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While your book may contain the answer to this question, the answer that you posted here does not. The text seems to be available via some other links. People interested in this topic should be aware of this text. Maybe the name of the author, the original publisher if any or a link to the aforementioned MAA review could be added to the answer in case he ever delete his account, but otherwise I don't see anything wrong with it.