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 foundamental subjects in category theory, and discuss it in connection with the notion of concrete category, with the notions of locally small and small fibration. We also discuss the appropriateness of our notion of concrete fibration for fibrations of small maps, relevantly to Algebraic Set Theory.
Concrete fibrations
PAGNAN, RUGGERO
In corso di stampa
Abstract
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 foundamental subjects in category theory, and discuss it in connection with the notion of concrete category, with the notions of locally small and small fibration. We also discuss the appropriateness of our notion of concrete fibration for fibrations of small maps, relevantly to Algebraic Set Theory.
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