A Generalised Exactness Structure for Sets
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arXiv
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| Format: | Preprint |
| Publié: |
2018
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| _version_ | 1866929701188009984 |
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| author | van Zyl, Phillip-Jan |
| author_facet | van Zyl, Phillip-Jan |
| contents | Two adjoint functors can be seen as generalisations of the two functions within a Galois connection. If instead the adjoints are not generalised from functions, but from relations, then analogously the object of study becomes a more general notion of an adjunction. A suitable method to express such functor-level relations is to consider functors into categories of families. This structure is then used to show that the central exactness structure in self-dual group theory, consisting of a chain of adjunctions, holds also for the category of sets when seen in this general form. EDIT: Please see the note about the empty set on page 4! |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1808_01350 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | A Generalised Exactness Structure for Sets van Zyl, Phillip-Jan Category Theory 18D99 (Primary) 18B05, 18A22, 18A32 (Secondary) Two adjoint functors can be seen as generalisations of the two functions within a Galois connection. If instead the adjoints are not generalised from functions, but from relations, then analogously the object of study becomes a more general notion of an adjunction. A suitable method to express such functor-level relations is to consider functors into categories of families. This structure is then used to show that the central exactness structure in self-dual group theory, consisting of a chain of adjunctions, holds also for the category of sets when seen in this general form. EDIT: Please see the note about the empty set on page 4! |
| title | A Generalised Exactness Structure for Sets |
| topic | Category Theory 18D99 (Primary) 18B05, 18A22, 18A32 (Secondary) |
| url | https://arxiv.org/abs/1808.01350 |