# Bruno Stonek

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bio website bruno.stonek.com location Montevideo, Uruguay age 25 member for 3 years, 11 months seen 51 mins ago profile views 1,985

Math student at UniversitÃ© Paris 13.

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 Mar28 comment Homotopy of Spectra Maps Induced by Homotopy of Functions Hi Jon, it's two and a half years in the future, and I've just slightly edited your post to fix some typos. I just wanted to let you know :) Mar28 revised Homotopy of Spectra Maps Induced by Homotopy of Functions added 2 characters in body Mar25 comment homotopic between two maps imply the homotopy between their mapping cone I'd like to point out that this is proved in much detail in proposition 3.2.15 in Arkowitz's Introduction to Homotopy Theory. Mar24 comment What is category theory? Your first paragraph can't really tell category theory apart from universal algebra, can it? Mar21 comment What does $1a \in Hom(a, a)$ mean? I think you could have answered this question yourself had you but looked a few pages before (or paragraphs above?) to see what is the definition of $1_a$ and of $\hom(a,a)$. Mar21 revised What does $1a \in Hom(a, a)$ mean? more descriptive title Mar21 answered Is complex exact if its Euler characteristic is zero? Mar19 comment Every module over a field is free. Is every commutative ring whose modules are all free a field? Here the question was asked for the more general non-commutative case. Mar19 answered Size Issues in Category Theory Mar18 revised Application of Composition of Functions: Real world examples? added 13 characters in body Mar18 answered Application of Composition of Functions: Real world examples? Mar18 comment Categorical introduction to Algebra and Topology To see Yoneda's lemma in action you should go into algebraic geometry, for example :) but for that you need to learn your basic abstract algebra first! Also, it is important to remember that not everything can be done/explained categorically. For example, a lot of the material in a standard introduction to group theory. Mar18 comment Categorical introduction to Algebra and Topology It does go beyond that. 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. Mar18 answered Categorical introduction to Algebra and Topology Mar18 answered Why is $\pi_1(\Bbb{R}^n,x_0)$ the trivial group in $\Bbb{R}^n$? Mar17 comment If a morphism of pushouts of complexes (with one arrow monic) is composed of quasi-isos, then the induced arrow is one also @Sunny: you're right, I wasn't clear enough. I mean one arrow monic in both pushout diagrams, yes. Mar16 comment How to prove a Set category with at least one element is a separator? Also, be careful, you say "a separator object for $f_1,f_2$", but that's not right. A separator is a separator for the category, and it satisfies the condition you wrote for every $f_1,f_2$. Mar16 comment How to prove a Set category with at least one element is a separator? @Problemania: $f(a)\neq g(a) \Rightarrow f\circ h(x)\neq g\circ h (x)$ since $a=h(x)$. Hence the two functions $f\circ h$ and $g\circ h$ are different at the element $x\in X$. If two functions differ in one point, then they are different, by definition of equality of functions! As for your second comment, yes, exactly, that's actually the definition of generator (or a slight rewording of it). Mar15 comment How to prove a Set category with at least one element is a separator? I'm not familiar with Lawvere's book, but I take it that he, as Johnstone, takes "separator" to mean what other categorical sources call "generator" . If it is not the case, then tell me and I'll delete the answer. Mar15 answered How to prove a Set category with at least one element is a separator?