4,216 reputation
21747
bio website bruno.stonek.com
location Montevideo, Uruguay
age 25
visits member for 3 years, 11 months
seen 18 hours ago

Math student at Université Paris 13.


Mar
24
comment What is category theory?
Your first paragraph can't really tell category theory apart from universal algebra, can it?
Mar
21
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 $\hom(a,a)$.
Mar
21
revised What does $1a \in Hom(a, a)$ mean?
more descriptive title
Mar
21
answered Is complex exact if its Euler characteristic is zero?
Mar
19
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.
Mar
19
answered Size Issues in Category Theory
Mar
18
revised Application of Composition of Functions: Real world examples?
added 13 characters in body
Mar
18
answered Application of Composition of Functions: Real world examples?
Mar
18
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.
Mar
18
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.
Mar
18
answered Categorical introduction to Algebra and Topology
Mar
18
answered Why is $\pi_1(\Bbb{R}^n,x_0)$ the trivial group in $\Bbb{R}^n$?
Mar
17
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.
Mar
16
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 $f_1,f_2$.
Mar
16
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).
Mar
15
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.
Mar
15
answered How to prove a Set category with at least one element is a separator?
Mar
15
reviewed Reject suggested edit on Why is the partial derivative $f_x' = 0 $ is not continous?
Mar
15
revised If a morphism of pushouts of complexes (with one arrow monic) is composed of quasi-isos, then the induced arrow is one also
added 526 characters in body; edited title
Mar
14
comment If a morphism of pushouts of complexes (with one arrow monic) is composed of quasi-isos, then the induced arrow is one also
Thank you. I will read your answer with detail later. I was just aware of "homotopy colimits" in the category of topological spaces, not in any more general sense.