Homotopy and homology of fibred spaces

We study fibred spaces with fibres in a structure category $\text{V}$ and we show that cellular approximation, Blakers–Massey theorem, Whitehead theorems, obstruction theory, Hurewicz homomorphism, Wall finiteness obstruction, and Whitehead torsion theorem hold for fibred spaces. For this we introduce the cohomology of fibred spaces.