Trying to implement schemes and homotopy

I have tried to describe an idea which includes sort of using the idea of Homotopy from Topology and Scheme from Algebraic Geometry; using only type signatures. I would like to ask if something like this can be implemented, and if anybody has done such a project.

I am quite new to Haskell. I am studying Programming with Categories by David Spivak, Brendan Fong and Bartosz Milewski. I am also studying Algebraic Geometry of Schemes. And I was wondering if something slightly abstract as such can be implemented in a useful way.