The present PhD thesis deals with the topic of relative topos theory over a base Grothendieck topos: the main goal is to show how the notions of comorphism of sites and of fibration provide an efficient formalism to study toposes over a base topos as toposes of relative sheaves. The main result in this work is the proof that fibrations over a base site (C,J) are 2-adjoint to toposes over the topos of sheaves Sh(C,J), and that this adjunction provides a 2-categorical generalization of the well known presheaf-bundle adjunction for topological spaces. The same adjunction is then specialized to presheaves, and provides a new description of the process of sheafification. Associating geometric morphisms to fibrations (seen as comorphisms of sites) also allows for an interpretation of toposes over a base as toposes of relative sheaves.

The present PhD thesis deals with the topic of relative topos theory over a base Grothendieck topos: the main goal is to show how the notions of comorphism of sites and of fibration provide an efficient formalism to study toposes over a base topos as toposes of relative sheaves. The main result in this work is the proof that fibrations over a base site (C,J) are 2-adjoint to toposes over the topos of sheaves Sh(C,J), and that this adjunction provides a 2-categorical generalization of the well known presheaf-bundle adjunction for topological spaces. The same adjunction is then specialized to presheaves, and provides a new description of the process of sheafification. Associating geometric morphisms to fibrations (seen as comorphisms of sites) also allows for an interpretation of toposes over a base as toposes of relative sheaves.

A foundation of relative topos theory via fibrations and comorphisms of sites / Riccardo Zanfa , 2021 Dec 14. 34. ciclo, Anno Accademico 2020/2021.

A foundation of relative topos theory via fibrations and comorphisms of sites

ZANFA, RICCARDO
2021-12-14

Abstract

The present PhD thesis deals with the topic of relative topos theory over a base Grothendieck topos: the main goal is to show how the notions of comorphism of sites and of fibration provide an efficient formalism to study toposes over a base topos as toposes of relative sheaves. The main result in this work is the proof that fibrations over a base site (C,J) are 2-adjoint to toposes over the topos of sheaves Sh(C,J), and that this adjunction provides a 2-categorical generalization of the well known presheaf-bundle adjunction for topological spaces. The same adjunction is then specialized to presheaves, and provides a new description of the process of sheafification. Associating geometric morphisms to fibrations (seen as comorphisms of sites) also allows for an interpretation of toposes over a base as toposes of relative sheaves.
14-dic-2021
The present PhD thesis deals with the topic of relative topos theory over a base Grothendieck topos: the main goal is to show how the notions of comorphism of sites and of fibration provide an efficient formalism to study toposes over a base topos as toposes of relative sheaves. The main result in this work is the proof that fibrations over a base site (C,J) are 2-adjoint to toposes over the topos of sheaves Sh(C,J), and that this adjunction provides a 2-categorical generalization of the well known presheaf-bundle adjunction for topological spaces. The same adjunction is then specialized to presheaves, and provides a new description of the process of sheafification. Associating geometric morphisms to fibrations (seen as comorphisms of sites) also allows for an interpretation of toposes over a base as toposes of relative sheaves.
A foundation of relative topos theory via fibrations and comorphisms of sites / Riccardo Zanfa , 2021 Dec 14. 34. ciclo, Anno Accademico 2020/2021.
File in questo prodotto:
File Dimensione Formato  
Tesi (3).pdf

accesso aperto

Descrizione: A foundation of relative topos theory via fibrations and comorphisms of sites ​
Tipologia: Tesi di dottorato
Dimensione 1.79 MB
Formato Adobe PDF
1.79 MB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/2128447
 Attenzione

L'Ateneo sottopone a validazione solo i file PDF allegati

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact