Abstract
If (ε, M)is a factorization system on a category C, we define new classes of maps as follows: a map f:A→B is in ε′ if each of its pullbacks lies in ε(that is, if it is stably in ε), and is in M * if some pullback of it along an effective descent map lies in M(that is, if it is locally in M). We find necessary and sufficient conditions for (ε′, M *) to be another factorization system, and show that a number of interesting factorization systems arise in this way. We further make the connexion with Galois theory, where M *is the class of coverings; and include self-contained modern accounts of factorization systems, descent theory, and Galois theory.
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Carboni, A., Janelidze, G., Kelly, G.M. et al. On Localization and Stabilization for Factorization Systems. Applied Categorical Structures 5, 1–58 (1997). https://doi.org/10.1023/A:1008620404444
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DOI: https://doi.org/10.1023/A:1008620404444