The category of matroids
The structure of the category of matroids and strong maps is investigated: it has coproducts and equalizers, but not products or coequalizers; there are functors from the categories of graphs and vector spaces, the latter being faithful and having a nearly full Kan extension; there is a functor to t...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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Springer Netherlands
2017
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| _version_ | 1797096876346966016 |
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| author | Heunen, C Patta, V |
| author_facet | Heunen, C Patta, V |
| author_sort | Heunen, C |
| collection | OXFORD |
| description | The structure of the category of matroids and strong maps is investigated: it has coproducts and equalizers, but not products or coequalizers; there are functors from the categories of graphs and vector spaces, the latter being faithful and having a nearly full Kan extension; there is a functor to the category of geometric lattices, that is nearly full; there are various adjunctions and free constructions on subcategories, inducing a simplification monad; there are two orthogonal factorization systems; some, but not many, combinatorial constructions from matroid theory are functorial. Finally, a characterization of matroids in terms of optimality of the greedy algorithm can be rephrased in terms of limits. |
| first_indexed | 2024-03-07T04:47:48Z |
| format | Journal article |
| id | oxford-uuid:d3e8696a-eafd-4673-97a3-689f787ca0e9 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T04:47:48Z |
| publishDate | 2017 |
| publisher | Springer Netherlands |
| record_format | dspace |
| spelling | oxford-uuid:d3e8696a-eafd-4673-97a3-689f787ca0e92022-03-27T08:14:34ZThe category of matroidsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:d3e8696a-eafd-4673-97a3-689f787ca0e9EnglishSymplectic Elements at OxfordSpringer Netherlands2017Heunen, CPatta, VThe structure of the category of matroids and strong maps is investigated: it has coproducts and equalizers, but not products or coequalizers; there are functors from the categories of graphs and vector spaces, the latter being faithful and having a nearly full Kan extension; there is a functor to the category of geometric lattices, that is nearly full; there are various adjunctions and free constructions on subcategories, inducing a simplification monad; there are two orthogonal factorization systems; some, but not many, combinatorial constructions from matroid theory are functorial. Finally, a characterization of matroids in terms of optimality of the greedy algorithm can be rephrased in terms of limits. |
| spellingShingle | Heunen, C Patta, V The category of matroids |
| title | The category of matroids |
| title_full | The category of matroids |
| title_fullStr | The category of matroids |
| title_full_unstemmed | The category of matroids |
| title_short | The category of matroids |
| title_sort | category of matroids |
| work_keys_str_mv | AT heunenc thecategoryofmatroids AT pattav thecategoryofmatroids AT heunenc categoryofmatroids AT pattav categoryofmatroids |