Recently, there was a post about the Euler characteristic of a type and other post about Hodge structure of a type. Then my questions are:
1) It is possible to construct characteristic classes (Wu, Stiefel-Whitney, Chern, Pontryagin classes) for an arbitrary type in HoTT?
2) It is possible to construct singular cohomology for a type and the corresponding Steenrod operations?
3) It is possible to construct an Aityah-Singer index theorem for an arbitrary type (a type fibered with other type).
4) It is possible to construct integrality theores for the characteristic numbers of an arbitrary fibered type?
Many thanks.
Juan Ospina
Medellín, Colombia