ABSTRACT

Intrinsically noncommutative spaces today are considered from the perspective of several branches of modern physics, including quantum gravity, string theory, and statistical physics. From this point of view, it is ideal to devise a concept of space and its geometry that is fundamentally noncommutative. Providing a clear introduction to noncommutat

chapter 1|10 pages

A Taste of Category Theory

chapter 2|68 pages

Noncommutative Spaces

chapter 3|32 pages

Grothendieck Categorical Representations

chapter 4|40 pages

Sheaves and Dynamical Topology