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Jan
4
suggested approved edit on How to prove hom functor preserves pullbacks
Dec
30
comment prove that two linear maps over a finite dimensional vector space are conjugate
isn't the category-theory tag a bit far-fetched?
Dec
30
comment Most important aspects of differential geometry for general relativity
Then you will need to learn differential...diagnostic and integral... nutrition :-)
Dec
29
answered Most important aspects of differential geometry for general relativity
Dec
29
asked Zorn's lemma in categorical language
Dec
29
comment How do morphisms in a comma category single out commuting squares?
This question has been posed before and fully answered by David Moews and me: math.stackexchange.com/a/98358/19609 . Unfortunately the title of that question was very vague, so it is not obvious what it is all about, by just browsing the site index. Basically most/all textbooks use a sloppy notation for a morphism in a comma category. The correct one should be a quadruple, as described in the cited reference or in Berci's answer below.
Dec
27
revised What is the benefit of the theory of categories?
edited some typos
Dec
27
suggested approved edit on What is the benefit of the theory of categories?
Dec
27
revised Understanding the Category of open subsets of a top. space X $Op_X$
edited some typos
Dec
27
suggested approved edit on Understanding the Category of open subsets of a top. space X $Op_X$
Dec
24
revised How to get used to commutative diagrams? (the case of products).
edited small typos
Dec
24
suggested approved edit on How to get used to commutative diagrams? (the case of products).
Dec
24
revised Uniqueness of morphism (reasoning in categorial language).
edited small typos
Dec
24
suggested approved edit on Uniqueness of morphism (reasoning in categorial language).
Dec
24
comment How to get used to commutative diagrams? (the case of products).
I have seen your edit. Still, if Aluffi is using this complicated definition, I suggest you switch to a proper category theory book, such as Awodey, where things are explained very simply. Also "the joy of cats" is very readable. Search my answers for links to online versions. Then get back to Aluffi for the purely algebraic part
Dec
24
comment How to get used to commutative diagrams? (the case of products).
This seems to be a very convoluted definition of the UMP of the product and I am not sure what you mean by "domain" of $f$ and $g$, which you say are objects (and so have no obvious domain). There are much simpler ones. Anyway, regarding commutative diagrams: please remember that these diagrams cannot fully replace a mathematical statement (which has quantifiers written in a specific order) and are basically used to help visualize the composing relations and the inner part of a mathematical statement (thus excluding the quantifiers).
Dec
24
comment Conglomeration for conglomeration's sake
Like @MartinBrandenburg, I never heard of 2-conglomerates either. Could you perhaps point out where you read/heard about them?
Dec
17
comment Pullbacks and the power set functor
With $\mathcal{P}_* D$ you mean the functor composition of $\mathcal{P}$ and $D$?
Nov
18
comment Taking the automorphism group of a group is not functorial.
Sorry Servaes, maybe I am missing something. Are you saying that $Aut$ works functorially almost everywhere in Grp except for some exotic group/group morphism that you cannot even remember right now?
Nov
18
comment If $T$ has an adjoint, why is $T(X\times Y)\simeq T(X)\times T(Y)$?
You start well Camilla, but you do not use the bonus universal arrows (unit and counit) that come with the adjunction. Stefan does that in his answer. Please note that your $\varphi$ is normally described as $\varphi^{-1}$ in the literature (you wrote the isomorphism in the opposite direction to the standard one). Please see CWM or Awodey. So your $\operatorname{rad}f$ is actually called a left adjunct $\operatorname{lad}f$ in the literature.