nLab localic homotopy theory

Idea

homotopy theory for locales (as opposed to, say topological homotopy theory or simplicial homotopy theory).

References

The fundamental group for locales is considered in

• W. He, Homotopy theory for locales, Acta Math. Sinica 46 (2003), no. 5

• J. F. Kennison, What is the fundamental group?, J. Pure Appl. Algebra 59(1989)

See also

• Erik Palmgren, From Intuitionistic to Point-Free Topology: On the Foundation of Homotopy Theory, Logicism, Intuitionism, and Formalism Volume 341 of the series Synthese Library pp 237-253, 2005 (pdf)