A cellular tower in SH or in a "more general stable homotopy category" is a chain of morphisms $\dots X^{(n)}\stackrel{g^n}{\to} X^{(n+1)}\to \dots$ along with some more data and conditions; one of them is that a cone/cofibre $C^n$ of $g^n$ should be a coproduct of spheres (of a certain sort). In the book "Spectra and the Steenrod Algebra" by H.R. Margolis the object $X^{(n)}$ is called an $n$-skeleton. Does there exist any name for $C^n$ (or maybe you can propose something "reasonable" for it?) - say, in algebraic topology? It appears that nobody calls it a "cell".
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asked Sep 22, 2021 at 18:52
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