Monic skeleta, Boundaries, Aufhebung, and the meaning of 'one-dimensionality'
Let E be a topos. If l is a level of E with monic skeleta then it makes sense to consider the objects in E that have l-skeletal boundaries. In particular, if p : E o S is a pre-cohesive geometric morphism then its centre (that may be called level 0) has monic skeleta. Let level 1 be the Aufhebung of...
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2019 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/128722 |
| Acceso en línea: | http://hdl.handle.net/11336/128722 |
| Access Level: | acceso abierto |
| Palabra clave: | Topos Theory Axiomatic Cohesion https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | Let E be a topos. If l is a level of E with monic skeleta then it makes sense to consider the objects in E that have l-skeletal boundaries. In particular, if p : E o S is a pre-cohesive geometric morphism then its centre (that may be called level 0) has monic skeleta. Let level 1 be the Aufhebung of level 0. We show that if level 1 has monic skeleta then the quotients of 0-separated objects with 0-skeletal boundaries are 1-skeletal. We also prove that in several examples (such as the classifier of non-trivial Boolean algebras, simplicial sets and the classifier of strictly bipointed objects) every 1-skeletal object is of that form. |
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