Notre Dame Journal of Formal Logic

Concrete Fibrations

Ruggero Pagnan

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As far as we know, no notion of concrete fibration is available. We provide one such notion in adherence to the foundational attitude that characterizes the adoption of the fibrational perspective in approaching fundamental subjects in category theory and discuss it in connection with the notion of concrete category and the notions of locally small and small fibrations. We also discuss the appropriateness of our notion of concrete fibration for fibrations of small maps, which is relevant to algebraic set theory.

Article information

Notre Dame J. Formal Logic, Volume 58, Number 2 (2017), 179-204.

Received: 30 June 2014
Accepted: 15 August 2014
First available in Project Euclid: 21 February 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 18A15: Foundations, relations to logic and deductive systems [See also 03- XX] 18A05: Definitions, generalizations
Secondary: 18B99: None of the above, but in this section

concrete fibration Isbell condition


Pagnan, Ruggero. Concrete Fibrations. Notre Dame J. Formal Logic 58 (2017), no. 2, 179--204. doi:10.1215/00294527-3817788.

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