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Mar
30
comment Interpretation of a formula and truth
Thanks Mauro! No need to excuse yourself for revamping an old question when it's done through a nice answer such as yours :)
Mar
30
awarded  Necromancer
Mar
28
awarded  Excavator
Mar
28
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 :)
Mar
28
revised Homotopy of Spectra Maps Induced by Homotopy of Functions
added 2 characters in body
Mar
25
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.
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 $f_1,f_2$.