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Yet another delooping machine

Bernard Badzioch·Kuerak Chung·Alexander A. Voronov
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Abstract

We suggest a new delooping machine, which is based on recognizing an n-fold loop space by a collection of operations acting on it, like the traditional delooping machines of Stasheff, May, Boardman-Vogt, Segal, and Bousfield. Unlike in the traditional delooping machines, which carefully select a nice space of such operations, we consider all natural operations on n-fold loop spaces, resulting in the algebraic theory Map (V_. S^n, V_. S^n). The advantage of this new approach is that the delooping machine is universal in a certain sense, the proof of the recognition principle is more conceptual, works the same way for all values of n, and does not need the test space to be connected.

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Bernard Badzioch, Kuerak Chung, Alexander A. Voronov. 2004-03-04. Yet another delooping machine. https://arxiv.org/abs/math/0403098

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