Continuous cohesion over sets
A pre-cohesive geometric morphism p : E → S satisfies Continuity if the canonical p!(Xp ∗S) → (p!X) S is an iso for every X in E and S in S. We show that if S = Set and E is a presheaf topos then, p satisfies Continuity if and only if it is a quality type. Our proof of this characterization rests on...
Guardado en:
| Autor principal: | |
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| Formato: | Articulo Preprint |
| Lenguaje: | Inglés |
| Publicado: |
2014
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| Materias: | |
| Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/99759 https://ri.conicet.gov.ar/11336/46008 http://www.tac.mta.ca/tac/volumes/29/20/29-20.pdf |
| Aporte de: |
| id |
I19-R120-10915-99759 |
|---|---|
| record_format |
dspace |
| institution |
Universidad Nacional de La Plata |
| institution_str |
I-19 |
| repository_str |
R-120 |
| collection |
SEDICI (UNLP) |
| language |
Inglés |
| topic |
Matemática Axiomatic cohesion Topos |
| spellingShingle |
Matemática Axiomatic cohesion Topos Menni, Matías Continuous cohesion over sets |
| topic_facet |
Matemática Axiomatic cohesion Topos |
| description |
A pre-cohesive geometric morphism p : E → S satisfies Continuity if the canonical p!(Xp ∗S) → (p!X) S is an iso for every X in E and S in S. We show that if S = Set and E is a presheaf topos then, p satisfies Continuity if and only if it is a quality type. Our proof of this characterization rests on a related result showing that Continuity and Sufficient Cohesion are incompatible for presheaf toposes. This incompatibility raises the question whether Continuity and Sufficient Cohesion are ever compatible for Grothendieck toposes. We show that the answer is positive by building some examples. |
| format |
Articulo Preprint |
| author |
Menni, Matías |
| author_facet |
Menni, Matías |
| author_sort |
Menni, Matías |
| title |
Continuous cohesion over sets |
| title_short |
Continuous cohesion over sets |
| title_full |
Continuous cohesion over sets |
| title_fullStr |
Continuous cohesion over sets |
| title_full_unstemmed |
Continuous cohesion over sets |
| title_sort |
continuous cohesion over sets |
| publishDate |
2014 |
| url |
http://sedici.unlp.edu.ar/handle/10915/99759 https://ri.conicet.gov.ar/11336/46008 http://www.tac.mta.ca/tac/volumes/29/20/29-20.pdf |
| work_keys_str_mv |
AT mennimatias continuouscohesionoversets |
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Repositorios |
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1764820493254262785 |