Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2407.17105 |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866911399900348416 |
|---|---|
| author | Kamio, Yuhi Hora, Ryuya |
| author_facet | Kamio, Yuhi Hora, Ryuya |
| contents | This paper solves the first of the open problems in topos theory posted by William Lawvere, concerning the existence of a Grothendieck topos that has proper class many quotient topoi. This paper concretely constructs such Grothendieck topoi, including the presheaf topos on the free monoid generated by countably infinitely many elements PSh(M_ω). Utilizing the combinatorics of the classifying topos of the theory of inhabited objects and with the help of a system of pairing functions, the problem is reduced to a theorem of Vopenka, Pultr, and Hedrlin, which states that any set admits a rigid relational structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_17105 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Solution to Lawvere's first problem: a Grothendieck topos that has proper class many quotient topoi Kamio, Yuhi Hora, Ryuya Category Theory 18F10, 18B25, 03C50 This paper solves the first of the open problems in topos theory posted by William Lawvere, concerning the existence of a Grothendieck topos that has proper class many quotient topoi. This paper concretely constructs such Grothendieck topoi, including the presheaf topos on the free monoid generated by countably infinitely many elements PSh(M_ω). Utilizing the combinatorics of the classifying topos of the theory of inhabited objects and with the help of a system of pairing functions, the problem is reduced to a theorem of Vopenka, Pultr, and Hedrlin, which states that any set admits a rigid relational structure. |
| title | Solution to Lawvere's first problem: a Grothendieck topos that has proper class many quotient topoi |
| topic | Category Theory 18F10, 18B25, 03C50 |
| url | https://arxiv.org/abs/2407.17105 |