2,150 reputation
618
bio website wildcatsformma.wordpress.com
location Somewhere over the rainbow
age
visits member for 2 years, 9 months
seen 22 hours ago

My scientific interests:

  • Mathematics: Category Theory, Algebra, Logic (Model-Theory, ATP), Control Systems
  • Physics: General Relativity, QFT
  • Amateur Astronomer and Astrophotographer
  • Mathematica programming

My Website:WildCats
Premiere Mathematica package for category theory

Visit the newly launched Mathematica.SE!

My non-scientific interests:

  • Skiing, Sailing, Windsurfing
  • Argentine Tango dancer

More or less fluent in (random order):

Italian, English, German, French, Spanish, Dutch and struggling with Russian


Mar
26
comment Distinguishing equality and isomorphism as relations
@alancalvitti By the way, in the upcoming release of WildCats, it will be possible to define isomorphisms within a category. Unfortunately i am experiencing a technical problem with my PC , so I cannot finalize the documentation.
Mar
26
comment Distinguishing equality and isomorphism as relations
@alancalvitti 1-anti-transitive? what do you mean? 2-Please write down how you would like to change the formula(s), so that we understand each other exactly.
Mar
25
comment Distinguishing equality and isomorphism as relations
@alancalvitti aha! Now I understand exactly what is the crux of your question. The isomorphism relation is reflexive, symmetric and transitive, but it is definitely not antisymmetric! So it is not a partial order. So it does not compete with the unique position held by equality, which is instead antisymmetric (besides being symmetric). Conclusion: the Wikipedia article is correct in saying that equality is the only reflexive, symmetric, antisymmetric and transitive relation.
Mar
25
comment Distinguishing equality and isomorphism as relations
Continued. Cat theory is nothing special. It is a theory with its axioms written in first order logic with equality. The equality sign appears directly in the axioms and is necessary in order to define composition and the dom and cod functions. You then define isomorphisms and it just happens that all important properties are conserved by isomorphisms, like all important topological properties are conserved by homeomorpisms (which are - not surprisingly - isomorphisms in $\bf Top$).
Mar
25
comment Distinguishing equality and isomorphism as relations
I knew @alancalvitti that most of what I wrote was probably known to you, but perhaps it will be useful for others. I have reread you question and I am not sure I understand what exactly is your issue here. I covered the linguistic/logic part, I think. So I just want to stress that in mathematics, also in set theory and also in cat theory, it is very clear and distinguishable when two "things" are equal, when they are not equal but they are "isomorphic" and when they are not equal and not isomorphic. Continued....
Mar
25
comment Distinguishing equality and isomorphism as relations
@alancalvitti I do not know who is Mazur and what comment of his you are referring to, but it is just wrong. In Set you have singleton {a} related by unique iso to singleton {b} yet a and b need not be equal. For ex. a might be $\emptyset$ and b might be {$\emptyset$}
Mar
25
revised Distinguishing equality and isomorphism as relations
Edited some small typos
Mar
24
awarded  Revival
Mar
24
answered Distinguishing equality and isomorphism as relations
Mar
21
comment Directed and projective limit in Rel
Hi Pieter and welcome to Math.SE ! What is the "I" in the formula n.2? In your first line you say "directed family of relations" what do you mean by this? On the other hand, in your 3rd line you say that this family only has the property of being "closed under concatenation". So which is which? Also "concatenation" means "composition in Rel", right? So this family could consist of just one arrow $R_{12}$? If yes, why do you call formula 1 infinite? Can you please give a reference where you found this problem?
Mar
16
comment Properties of the Category of topological spaces with $n$ basepoints.
I thought so, thank you @MartinBrandenburg
Mar
14
comment Properties of the Category of topological spaces with $n$ basepoints.
@MartinBrandenburg Is B a generic topological space? I mean: any topology? any cardinality?
Mar
14
comment Equivalence of categories of coalgebras
Hello user66685, welcome to Mathematics.SE . I would suggest you take a moment to think about a more personalized nickname than the automatic one you have been assigned
Mar
14
comment Forgetful Functors Create Limits
Good problem, could you please give a reference where does it come from?
Mar
12
awarded  Civic Duty
Mar
9
awarded  Revival
Mar
8
revised If we have an equivalence relation on a class, is it possible to define what it means for the collection of equivalence “to be a set”?
edited antecedent formula
Mar
8
suggested suggested edit on If we have an equivalence relation on a class, is it possible to define what it means for the collection of equivalence “to be a set”?
Mar
6
comment If $C'$ is a subcategory of $C$, why can $\mathrm{Hom}_C(X, Y)$ and $\mathrm{Hom}_{C'}(X, Y)$ be different?
I edited your first formula, since it was written backwards
Mar
6
revised If $C'$ is a subcategory of $C$, why can $\mathrm{Hom}_C(X, Y)$ and $\mathrm{Hom}_{C'}(X, Y)$ be different?
edited subset formula