When is a category of adherence-determined convergences simple?
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866909586681757696 |
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| author | Mynard, Frédéric Wojciechowski, Jerzy |
| author_facet | Mynard, Frédéric Wojciechowski, Jerzy |
| contents | Abstract. We provide a characterization of classes of filters $\mathbb{D}$ for which the full subcategory $\operatorname{fix}\operatorname{A}_{\mathbb D}$ of $\mathsf{Conv}$ formed by convergences determined by the adherence of filters of the class $\mathbb{D}$ is simple in $\mathsf{Conv}$. Along the way, we also elucidate when two classes of filters result in the same category of adherence-determined convergences. As an application of the main result, we show that the category of hypotopologies is not simple, thus answering a question from [25]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_11954 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | When is a category of adherence-determined convergences simple? Mynard, Frédéric Wojciechowski, Jerzy General Topology Category Theory 54A20, 54B30 Abstract. We provide a characterization of classes of filters $\mathbb{D}$ for which the full subcategory $\operatorname{fix}\operatorname{A}_{\mathbb D}$ of $\mathsf{Conv}$ formed by convergences determined by the adherence of filters of the class $\mathbb{D}$ is simple in $\mathsf{Conv}$. Along the way, we also elucidate when two classes of filters result in the same category of adherence-determined convergences. As an application of the main result, we show that the category of hypotopologies is not simple, thus answering a question from [25]. |
| title | When is a category of adherence-determined convergences simple? |
| topic | General Topology Category Theory 54A20, 54B30 |
| url | https://arxiv.org/abs/2112.11954 |