Journal article

The category of matroids

Abstract:: 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.

Publication status:: Published

Peer review status:: Peer reviewed

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APA Style

Heunen, C., & Patta, V. (2017). The category of matroids. Applied Categorical Structures, 26(2), 205–237.

MLA Style

Heunen, C., and V. Patta. “The Category of Matroids.” Applied Categorical Structures, vol. 26, no. 2, Springer Netherlands, 2017, pp. 205–37.

Chicago Style

Heunen, C, and V Patta. 2017. “The Category of Matroids.” Applied Categorical Structures 26 (2): 205–37.
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Files:: Heunen, C and Patta, V, (2017) Applied Categorical Structures.pdf

(Preview, Version of record, pdf, 942.6KB, Terms of use)

Publisher copy:: 10.1007/s10485-017-9490-2

Authors

+ Heunen, C More by this author

Role:: Author

+ Patta, V More by this author

Institution:: University of Oxford
Division:: MPLS
Department:: Computer Science
Role:: Author

+ Engineering and Physical Sciences Research Council More from this funder

Funding agency for:: Patta, V
Grant:: EP/K503113/1

Publisher:: Springer Netherlands
Journal:: Applied Categorical Structures More from this journal
Volume:: 26
Issue:: 2
Pages:: 205–237
Publication date:: 2017-04-20
Acceptance date:: 2017-03-29
DOI:: 10.1007/s10485-017-9490-2
EISSN:: 1572-9095
ISSN:: 0927-2852

Language:: English
Keywords:: category theory

matroids
Pubs id:: pubs:690954
UUID:: uuid:d3e8696a-eafd-4673-97a3-689f787ca0e9
Local pid:: pubs:690954
Source identifiers:: 690954
Deposit date:: 2017-04-22

Terms of use

Copyright holder:: Heunen and Patta
Copyright date:: 2017
Notes:: Copyright © 2017 The Authors.

This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Licence:: CC Attribution (CC BY)

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