Topological and algebraic pullback functors

2012/05/14 by Jack S. Calcut, John D. McCarthy, Calcut, Jack S. +3
Mathematics · #05E18 (Primary) 18A22 #19A22 (Secondary) #57M10 #Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics #Group Theory (math.GR) #math.AT #math.CT #math.GR #msc:05E18 #msc:18A22 #msc:19A22 #msc:57M10

paper · pdf · doi:10.48550/arxiv.1205.3121

27 pages, 3 figures

arxiv created 2012/05/14 · arxiv updated 2012/05/15

Abstract

We give algebraic equivalents for certain desirable properties of pullback functors on categories of coverings and group sets, namely nullity zero, essential injectivity, and essential surjectivity. Nullity zero turns out to be equivalent to the notion of a contranormal subgroup. We observe a Tannakian-like phenomenon with essential injectivity. Essential surjectivity is intimately related to Zappa-Szép products. We include several examples, and some open questions.

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