It is a fairly standard result that any map $f:X \rightarrow Y$ can be represented by composition of two maps $X \rightarrow Z \rightarrow Y$ where either the first is cofibration and the second one is homotopy equivalence or the first one is homotopy equivalence and the latter is a fibration. Is it true that any map can be decomposed as a composition of cofibration and fibration? Can we impose some additional conditions for instance that the cofibration is an $n$-equivalence?
2026-03-29 03:12:17.1774753937
Representing map as a composition of cofibration and fibration
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