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Jul
29
comment Identity of Initial Elements in a Category
the comment by @Kris , taken at face value, is meaningless. Established mathematical theories (like Category theory) are always logically consistent. otherwise they are discarded right away (just like Frege's naive set theory). Category theory is based on logic with equality and equality is used extensively for ex. to test whether a morphism is monic or epic. The point of category theory, as explained also by Qiaochu Yuan, is that the properties that we should care about should be invariant for isomorphic objects....
Jul
26
revised Proof in Hungerford about natural isomorphisms of multifunctors
edited formula
Jul
26
suggested approved edit on Proof in Hungerford about natural isomorphisms of multifunctors
Jul
26
comment Proof in Hungerford about natural isomorphisms of multifunctors
It does hold for multifuntors too. The author just wants you to write down the (more general) equations in this case. I would replace "equivalence" with "isomorphism" in your text and perhaps use the more common id in place of $\varepsilon$ .
Jul
24
comment An example of a monomorphism that is not an equalizer in “Abstract and Concrete Categories — The Joy of Cats”
did they answer to your mail?
Jul
9
revised Clarification of the Definiton of Locally Small Categories
Added last paragraph
Jul
9
answered Clarification of the Definiton of Locally Small Categories
Jul
4
revised To what extent are morphisms required to be functions?
Added more detail on dom and cod
Jul
4
answered To what extent are morphisms required to be functions?
Jun
12
comment is there a property of a category that is preserved by category isomorphism, but not equivalence?
+1 Nice examples too!
Jun
12
comment is there a property of a category that is preserved by category isomorphism, but not equivalence?
+1 Nice examples!
Jun
7
answered English-Italian translations of “sieve” and “sink” in sheaf theory
May
27
comment Category theory for sensorimotor learning?
The word "sensorimotor" in the title, is a technical term or a typo? If it is a typo you might wish to edit it.
May
25
comment How does one show that two functors are *not* isomorphic?
@MarianoSuárez-Alvarez..... This may or may not be easier, but is certainly a different problem, thus not a tautology. Awodey gives an explicit example of this with posets.I realize that my answer is very general, but so appears to be (some of) the OP's questions (title and 3rd paragraph). You and others have covered the specific examples mentioned in the rest of the Op's post. By the way, I do appreciate your smiley, we are all here to help and learn from each other in a relaxed atmosphere :-)
May
25
comment How does one show that two functors are *not* isomorphic?
@MarianoSuárez-Alvarez I was not aware of a comment mentioning invariants. I looked at this question only a few hours ago and I did not see that comment. Please note that I plainly said that this procedure is applicable to anything, as long as you can see the * any things* as objects in a suitable category. The rest of my answer is not a tautology. It is a consequence of the Yoneda lemma. I simply emphasized that: to see whether 2 objects are isomorphic, you can check whether the respective Yoneda embeddings are isomorphic. Cont....
May
25
comment How does one show that two functors are *not* isomorphic?
what is the question in your opinion @MartinBrandenburg ?
May
25
answered How does one show that two functors are *not* isomorphic?
May
21
comment A basic doubt on axiom of foundation of Zermelo-Fraenkel set theory
MarkS. and @AsafKaragila I know, I know, but I was under the impression that the OP thought it was relatively easy to come up with such a set S, so I encouraged him to actually do it.
May
21
answered A basic doubt on axiom of foundation of Zermelo-Fraenkel set theory
May
20
comment Preserving structures
great answer and great examples!