The n-Category Café

I’m imagining that dialog in the Big Seminar in the Sky where Dan Kan and Archimedes talk about simplicial homotopy theory. Explaining the real numbers comes later.

Unfortunately, it is a fact that «the philosophy of mathematics of past century did not want to know anything about its inner life». This led to the position that it became «hard to envisage internally-driven change».

Yet there is still a hope for «the dynamic interplay between mathematics and physics, each with their rich inner lives». Otherwise, «all mathematical activity is just some sort of proof machine».

Obviously, you shouldn’t be limited only to physics. But that is not the question.

Recognizing the dialectic between theoretical and applied sciences and mathematics, by adding philosophical aspects to it, we are interested in the issues that connect these disciplines. It will allow to «make the most informed decisions about our own methods and concepts».

Among these methods I will firstly point out cohomology and higher category. There are authoritative opinions regarding those. In particular, Eberhard Zeidler and Urs Schreiber, which indicate their ability to play a fundamental research role, for example, in physics.

But the problem is that there is still a disconnection between mathematics and scientific disciplines, especially when it comes to the application of algebraic methods. It is natural. And therefore, any steps aimed at bringing them closer are encouraging.