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Very-Well-Behaved Epireflections for Categories of Models of Sketches
Jo\~ao J. Xarez
https://arxiv.org/abs/2509.07241 https://arxiv.org/pdf/2509.07241

Very-Well-Behaved Epireflections for Categories of Models of Sketches
Firstly, precise conditions on how to obtain very-well-behaved epireflections are explored and improved from the author's previous papers; meaning that, beginning with a monad and a prefactorization system on a category, is produced a reflection with stable units (stronger than semi-left-exactness, also called admissibility in categorical Galois Theory) and an associated monotone-light factorization. Then, we were able to show that, for a pseudo-filtered category J in which every arrow is a mon…