Let $A$ be the subcomplex of a CW complex $X$, let $Y$ be a CW complex, let $f: A \to Y$ be a cellular map, and let $Y \cup_f X$ be the pushout of $f$ and the inclusion $A \to X$. My question is, is $Y \cup_f X$ a CW complex with $Y$ as a subcomplex and $X/A$ as a quotient complex?
2025-01-12 23:31:36.1736724696
Is $Y \cup_f X$ a CW complex?
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