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8 $begingroup$ I use a custom function/head Operator[low, high] which encodes a generic polynomial expression split into "low" and "high" summands following considerations which are irrelevant to this question. Two Operator objects should sum in the following way: Operator[a,b] + Operator[c,d] -> Operator[a+c,b+d] which is just standard element–wise summation that List does automatically. How can I tell Mathematica that this kind of automatic simplification or rearrangement is not only allowed, but desirable? function-construction share | improve this question asked Dec 21 '18 at 15:12

13 7 $begingroup$ I am new to H-spaces, delooping, etc. I know that not every $H$ -space has a delooping (e.g. Stasheff's theorem, one needs a group-like $A_infty$ space). I also know that the same space can have inequivalent deloopings corresponding to different $H$ -space structures. An example is $BU$ , which has two $H$ -space structures (coming from direct sum, respectively tensor product, of vector bundles). Once you fix an $H$ -space structure on a space $X$ , is there at most one (up to homotopy) delooping $BX$ such that $X$ and $Omega BX$ are equivalent as $H$ -spaces, in some appropriate sense? homotopy-theory stable-homotopy share | cite | improve this question