Let $f:A\rightarrow B, g:B\rightarrow C$ be maps in the category CGWH (compactly generated weakly Hausdorff spaces). Do we have a homotopy fibration sequence
$$F(f)\rightarrow F(gf) \rightarrow F(g)$$
consisting of homotopy fibres? (And the dual statement for homotopy cofibres?)



Homotopy fibre of composition
This is a fundamental and basic property in homotopy theory, as is the dual statement for homotopy cofibers. These appear as Lemmas 1.2.7 and 1.2.5 in the recently published book *More concise algebraic topology* by May and Ponto. (And in stable model categories these merge and become the octahedral axiom.)


