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bio website wildcatsformma.wordpress.com
location Somewhere over the rainbow
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visits member for 2 years, 8 months
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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
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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


Jul
5
comment Category of metric spaces versus category of non-empty spaces
@egreg could you please be clearer: do you prefer $\mathbf{Met}$ or $\mathbf{Met}_{\not=\emptyset}$ ?
Jun
30
comment Can I define a category as a monoid with partially defined multiplication?
It is more productive to think the other way around: a monoid is a category with just one object. So all proofs you have for categories are valid for monoids (plus there are others which only hold for monoids)
Jun
30
comment Collection vs set in this textbook about category theory, and some related questions.
Which textbook?
Jun
24
comment Is there such a thing as 'overtification' (dual to compactification)?
David: any duality principle relies on the logical structure of the axioms involved. So it relies on the quantifiers and logical connectives forming the axioms. This is no exception.
Jun
24
comment Is there such a thing as 'overtification' (dual to compactification)?
I join @MartinBrandenburg in asking more overtness in this definition :-)
Jun
20
comment Adjoint situation induced on presheaves
Thank you Pece. I managed to guess your first paragraph on my own, but I am/was not very familiar with the Kan extensions concept and notation
Jun
15
comment What is the use of generators of a category?
The terminology was "poorly chosen" (Maclane's words). A better name would be "separator" or "discriminator" (my word), because it helps discriminate one morphism from another
Jun
14
comment Is the comma category $y \downarrow X$ small?
Pece: I know, you know but...does everybody know? Indeed the OP explicitly asked for that.
Jun
13
comment Is the comma category $y \downarrow X$ small?
nice! perhaps you could also add the proof that the homs in the comma category are small sets and thus show that the comma category is indeed small
Jun
11
comment Left & right adjoints in the context of posets.
@OlivierBégassat "I can never remember which": Awodey teaches "Right adjoints preserve limits = RAPL". So just remember RAPL and use duality for left adjoints
Jun
5
comment Uniqueness of the Comparison Functor
@Chilango you are welcome, my pleasure :-)
Jun
4
comment Uniqueness of the Comparison Functor
what does it mean $U\in D$ ? $U$ is a functor and $D$ is a category
Jun
4
comment Types, Sets and Categories
@CristianGarcia I am glad :-)
May
25
comment Exercise from Rotman, direct limit of quotient modules
@WLOG Thank you :-)
May
25
comment Exercise from Rotman, direct limit of quotient modules
@WLOG Could you please write where is this exercise in Rotman?
May
24
comment Showing that a diagram commutes in the most economical way
@R.N. It is a generalization of the situation depicted by Pece in his comment above
May
23
comment Showing that a diagram commutes in the most economical way
@R.N. I added an optimization procedure, perhaps this is what you were looking for
May
23
comment Showing that a diagram commutes in the most economical way
@LeenDroogendijk What is a "directed $P_5$...." ? In any case, you (might) have a special category, but the question is very clear, in the last paragraph it says:"In general, given a diagram....", so your (or any other) special example is not relevant to the OP.
May
14
comment For which values of $a$ is this set a manifold?
No Cure , Jeremy's answer is correct. I was referring to what you wrote in your question.
May
12
comment Diffeomorphic connected hypersurfaces
To give $A^\mu$ a chance to exist, it should be on the plane spanned by $n'$ and $n$