Functorial embeddings associated with the Four Subspace Problem
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917363245383680 |
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| author | Dorado, Ivon Medina, Gonzalo |
| author_facet | Dorado, Ivon Medina, Gonzalo |
| contents | We define a unified categorical framework for studying six subproblems arising from the classical Four Subspace Problem. For each subproblem, we construct a functor from its associated category to the category of representations of the quiver corresponding to the Four Subspace Problem. This approach gives a common structural setting for the six cases considered and allows a simultaneous and coherent analysis via functorial methods.
We prove that the six functors are additive and fully faithful, and we show that none of them is dense. As a consequence, each functor induces an equivalence between the corresponding source category and a well-identified full subcategory of the target category. These equivalences provide an effective mechanism for transferring classification results and structural properties, thereby clarifying the structural interrelations among the categories studied. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_25676 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Functorial embeddings associated with the Four Subspace Problem Dorado, Ivon Medina, Gonzalo Representation Theory 16G20 (Primary), 18A25 (Secondary) We define a unified categorical framework for studying six subproblems arising from the classical Four Subspace Problem. For each subproblem, we construct a functor from its associated category to the category of representations of the quiver corresponding to the Four Subspace Problem. This approach gives a common structural setting for the six cases considered and allows a simultaneous and coherent analysis via functorial methods. We prove that the six functors are additive and fully faithful, and we show that none of them is dense. As a consequence, each functor induces an equivalence between the corresponding source category and a well-identified full subcategory of the target category. These equivalences provide an effective mechanism for transferring classification results and structural properties, thereby clarifying the structural interrelations among the categories studied. |
| title | Functorial embeddings associated with the Four Subspace Problem |
| topic | Representation Theory 16G20 (Primary), 18A25 (Secondary) |
| url | https://arxiv.org/abs/2603.25676 |