Dropping support for that stuff means breaking 95% of the websites people currently use. It's a non-starter, it cannot ever happen, even if you think it would be for the best.
kogasa
joined 2 years ago
Math builds up so much context that it's hard to avoid the use of shorthand and reused names for things. Every math book and paper will start with definitions. So it's not really on you for not recognizing it here
🍕(--, B) : C -> Set denotes the contravariant hom functor, normally written Hom(--, B). In this case, C is a category, and B is a fixed object in that category. The -- can be replaced by either an object or morphism of C, and that defines a map from C to Set.
For any given object X in C, the hom-set Hom(X, C) is the set of morphisms X -> B in C. For a morphism f : X -> Y in C, the Set morphism Hom(f, B) : Hom(Y, B) -> Hom(X, B) is defined by sending each g : Y -> B to gf : X -> B. This is the mapping C -> Set defined by Hom(--, C), and it's a (contravariant) functor because it respects composition: if h : X -> Y and f : Y -> Z then fh : X -> Z and Hom(fh, C) = Hom(h, C)Hom(f, C) sends g : Z -> B to gfh : X -> B.
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P^(n)(R) AKA RP^n is the n-dimensional real projective space.
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The caveat "phi is a morphism" is probably just to clarify that we're talking about "all morphisms X -> Y [in a given category]" and not simply all functions or something.
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For more context, the derived functor of Hom(--, B) is called the Ext functor, and the exactness of that sequence (if the typo were fixed) is the statement of the universal coefficient theorem (for cohomology): https://en.wikipedia.org/wiki/Universal_coefficient_theorem The solution to this problem is the "Example: mod 2 cohomology of the real projective space" on that page. It's (Z/2Z)[x] / <x^(n+1)> or 🍔[x]/<x^(n+1)>, i.e. the ring of polynomials of degree n or less with coefficients in 🍔 = Z/2Z, meaning coefficients of 0 or 1.
It's not nonsense, although there is a typo that makes it technically unsolvable. If you fix the typo, it's an example calculation in the wikipedia page on the universal coefficient theorem: https://en.m.wikipedia.org/wiki/Universal_coefficient_theorem
It's real projective space
The standard .NET C# compiler and CLI run on and build for Windows, MacOS, and Linux. You can run your ASP.NET webapps in a Linux docker container, or write console apps and run them on Linux, it doesn't matter anymore. As a .NET dev I have literally no reason to ever touch Windows, unless I'm touching legacy code from before .NET Core or building a Windows-exclusive app using a Windows app framework.
Ok, there's no such thing as native Windows apps for Linux, but there are cross platform GUI frameworks like Avalonia and Uno that can produce apps with a polished identical experience across all platforms, no electron needed
It's fully cross platform with .NET Core and later.
It's on purpose. They're trying to avoid calling them people. Not illegal immigrants anymore, just illegals. Not trans people, just things. Yes, the implications of intentional dehumanization are horrific beyond imagination.
Nice pic
Some of it looks like topology. The curvy horizontal lines turning into curvy vertical lines are symbols relating to the Kauffman bracket, which belongs to knot theory.
https://encyclopediaofmath.org/wiki/Kauffman_bracket_polynomial
It's a different situation, as a dev I'd happily bet my life on this assumption.