Topological and algebraic pullback functors
Algebraic Topology
2012-05-15 v1 Category Theory
Group Theory
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-Sz{\'e}p products. We include several examples, and some open questions.
Keywords
Cite
@article{arxiv.1205.3121,
title = {Topological and algebraic pullback functors},
author = {Jack S. Calcut and John D. McCarthy and Jeremy J. Walthers},
journal= {arXiv preprint arXiv:1205.3121},
year = {2012}
}
Comments
27 pages, 3 figures