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Algebraic theories in homotopy theory
 Annals of Math
"... It is well known in homotopy theory that given a loop space X one can always find a simplicial group G weakly equivalent to X, such that the weak equivalence can be realized by maps preserving multiplication. It is also known that loop spaces are not the only class of spaces for which result of this ..."
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It is well known in homotopy theory that given a loop space X one can always find a simplicial group G weakly equivalent to X, such that the weak equivalence can be realized by maps preserving multiplication. It is also known that loop spaces are not the only class of spaces for which result of this kind holds; for example, any
From Γspaces to algebraic theories
, 2003
"... In [13] Segal gave the following elegant characterization of infinite loop spaces. Let Γop be the category whose objects are finite sets [n] = {0, 1,..., n} for n ≥ 0 and whose morphisms are all maps of sets ϕ: [n] → [m] satisfying ϕ(0) = 0. For n> 1 and 1 ≤ k ≤ n let pn k: [n] → [1] be the m ..."
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In [13] Segal gave the following elegant characterization of infinite loop spaces. Let Γop be the category whose objects are finite sets [n] = {0, 1,..., n} for n ≥ 0 and whose morphisms are all maps of sets ϕ: [n] → [m] satisfying ϕ(0) = 0. For n> 1 and 1 ≤ k ≤ n let pn k: [n] → [1] be the map such that pn k