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Archive for Mathematical Logic

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

Splitting idempotents in a fibered setting

  • Ruggero PagnanEmail author
Article
  • 30 Downloads

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

Keywords

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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