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  "body": "\n## Summary\n\nAn infinite loop space is a space $X$ that is the [[loop space|2JFF5F3EGF]] of a space.\nThat space is again a loop space, and so on without end.\nInfinite loop spaces are exactly the zeroth spaces of $\\Omega$-spectra, so they are the unstable shadows of [[spectra|1GHF4EKBXS]] and of generalized cohomology theories.\nRecognition principles, such as the [[May recognition principle|5SMK5KEBQE]], detect them by a homotopy-coherent commutative multiplication.\n\n## Explanations\n\n### L1 human\n\nLoops in a space can be composed, so a loop space has a multiplication that is associative up to homotopy.\nIf the space is a double loop space, the multiplication is also commutative up to homotopy.\nAn infinite loop space has infinitely many such layers of structure, which make its multiplication as commutative as homotopy theory allows.\nFor an abelian group $A$, the Eilenberg–MacLane spaces $K(A, n)$ satisfy $K(A, n) \\simeq \\Omega K(A, n+1)$, so each of them is an infinite loop space.\n",
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