Abstract
In this article the notion of quasi left factorization structure in a category \({\mathcal{X}}\) is given. It is proved that quasi left factorization structures correspond to subobjects of a predefined object in the category of laxed preordered valued presheaves, \(\boldsymbol{L}ax({PrOrd}^{{\boldsymbol{\mathcal{X}}}^{op}})\). The main result proves this correspondence is one to one when quasi left factorization structures are restricted to the so called QLF-codomains.
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Hosseini, S.N., Mousavi, S.S. Quasi Left Factorization Structures as Presheaves. Appl Categor Struct 22, 501–514 (2014). https://doi.org/10.1007/s10485-013-9316-9
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DOI: https://doi.org/10.1007/s10485-013-9316-9