Abstract
By splitting idempotent morphisms in the total and base categories of fibrations we provide an explicit elementary description of the Cauchy completion of objects in the categories Fib(\(\mathbb {B}\)) of fibrations with a fixed base category \(\mathbb {B}\) and Fib of fibrations with any base category. Two universal constructions are at issue, corresponding to two fibered reflections involving the fibration of fibrations \(\mathbf{Fib}\rightarrow \mathbf{Cat}\).
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Pagnan, R. Splitting idempotents in a fibered setting. Arch. Math. Logic 57, 917–938 (2018). https://doi.org/10.1007/s00153-018-0616-5
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DOI: https://doi.org/10.1007/s00153-018-0616-5