We prove that, in the category of groups, the composition of a cellularization and a localization functor need not be idempotent. This provides a negative answer to a question of Emmanuel Dror Farjoun.
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Hokkaido Univ, Fac Sci, Dept Math, Kita 10, Nishi 8, Kita Ku, Sapporo, Hokkaido 0600810, JapanTokyo Univ Sci, Fac Sci Div 2, Dept Math, 1-3 Kagurazaka,Shinjuku Ku, Tokyo 1628601, Japan
Akita, Toshiyuki
Kawasaki, Rikako
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Tokyo Univ Sci, Fac Sci Div 2, Dept Math, 1-3 Kagurazaka,Shinjuku Ku, Tokyo 1628601, JapanTokyo Univ Sci, Fac Sci Div 2, Dept Math, 1-3 Kagurazaka,Shinjuku Ku, Tokyo 1628601, Japan
Kawasaki, Rikako
Satoh, Takao
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Tokyo Univ Sci, Fac Sci Div 2, Dept Math, 1-3 Kagurazaka,Shinjuku Ku, Tokyo 1628601, JapanTokyo Univ Sci, Fac Sci Div 2, Dept Math, 1-3 Kagurazaka,Shinjuku Ku, Tokyo 1628601, Japan