The Internal Logic and Finite Colimits
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866915243634982912 |
|---|---|
| author | Troiani, William |
| author_facet | Troiani, William |
| contents | We describe how finite colimits can be described using the internal lanuage, also known as the Mitchell-Benabou language, of a topos, provided the topos admits countably infinite colimits. This description is based on the set theoretic definitions of colimits and coequalisers, however the translation is not direct due to the differences between set theory and the internal language, these differences are described as internal versus external. Solutions to the hurdles which thus arise are given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_10805 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Internal Logic and Finite Colimits Troiani, William Logic 18C20 We describe how finite colimits can be described using the internal lanuage, also known as the Mitchell-Benabou language, of a topos, provided the topos admits countably infinite colimits. This description is based on the set theoretic definitions of colimits and coequalisers, however the translation is not direct due to the differences between set theory and the internal language, these differences are described as internal versus external. Solutions to the hurdles which thus arise are given. |
| title | The Internal Logic and Finite Colimits |
| topic | Logic 18C20 |
| url | https://arxiv.org/abs/2504.10805 |