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Lao-tzu
Lao-tzu
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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 fibrefibration sequence $$F(f)\rightarrow F(gf) \rightarrow F(g)$$ consisting of homotopy fibres? (And the dual statement for homotopy cofibres?)

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 fibre sequence $$F(f)\rightarrow F(gf) \rightarrow F(g)$$ consisting of homotopy fibres?

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?)

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Lao-tzu
Lao-tzu
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Homotopy fibre of composition

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 fibre sequence $$F(f)\rightarrow F(gf) \rightarrow F(g)$$ consisting of homotopy fibres?