Category of Noncommutative CW Complexes

TL;DR

This paper introduces noncommutative CW complexes, defining key constructions like mapping cylinders and cones, and proves an approximation theorem with applications to homotopy sequences in noncommutative topology.

Contribution

It formalizes the concept of noncommutative CW complexes and establishes foundational theorems including the noncommutative Approximation Theorem.

Findings

Defined noncommutative CW complexes

Proved the noncommutative Approximation Theorem

Derived long exact homotopy sequences

Abstract

We expose the notion of noncommutative CW (NCCW) complexes, define noncommutative (NC) mapping cylinder and NC mapping cone, and prove the noncommutative Approximation Theorem. The long exact homotopy sequences associated with arbitrary morphisms are also deduced.