# All Questions

98,519 questions
2k views

### Closest grid square to a point in spherical coordinates

I am programming an algorithm where I have broken up the surface of a sphere into grid points (for simplicity I have the grid lines are parallel and perpendicular to the meridians). Given a point A on ...
16k views

### What is inter-universal geometry?

I wonder what Mochizuki's inter-universal geometry and his generalisation of anabelian geometry is, e.g. why the ABC-conjecture involves nested inclusions of sets as hinted in the slides, or why such ...
1k views

### Conjugation in SU(2)

For any two matrices $P,Q \in SU(2)$, with $tr(P)=tr(Q)=0$, does there always exist some $G\in SU(2)$ such that $G P G^{-1} = -P$, and $G Q G^{-1} = -Q\ ?$
2k views

### Is any representation of a finite group defined over the algebraic integers?

Apologies in advance if this is obvious.
2k views

### The core question of topology

As I see it, the core question of topology is to figure out whether a homeomorphism exists between two topological spaces. To answer this question, one defines various properties of a space such as ...
430 views

19k views

### What is (co)homology, and how does a beginner gain intuition about it?

This question comes along with a lot of associated sub-questions, most of which would probably be answered by a sufficiently good introductory text. So a perfectly acceptable answer to this question ...
921 views

### Quotient of a category by a free group action

Let Cat denote the 1-category of small categories. The functor Mor : Cat -> Set which assigns to a category its set of morphisms (aka Hom([• -> •], -)) does not commute with most colimits. ...