Archive for Mathematical Logic

, Volume 57, Issue 7–8, pp 917–938 | Cite as

Splitting idempotents in a fibered setting

  • Ruggero PagnanEmail author


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 \(\mathbf{Fib}\rightarrow \mathbf{Cat}\).


Category Idempotent Cauchy completion Fibration 

Mathematics Subject Classification

1802 18A15 18A05 18B99 


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.DIMAUniversity of GenovaGenoaItaly

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