2015/12/31 by Chris Heunen, Vaia Patta · 13 citations
Computer Science · Decision Sciences · Mathematics · #Adjoint functors #Advanced Algebra and Logic #Characterization (materials science) #Concrete category #Coproduct #Functor #Functor category #Fuzzy and Soft Set Theory #Graphic matroid #Homotopy and Cohomology in Algebraic Topology #Matroid #math.CO #math.CT
paper · pdf · doi:10.1007/s10485-017-9490-2
published in Applied Categorical Structures 26(2), 205-237 (Springer Science+Business Media) · 31 pages, 10 diagrams, 28 references
openalex created_date 2016/06/24 · openalex publication_date 2017/04/20 · arxiv created 2018/09/23 · arxiv updated 2020/12/03 · openalex updated_date 2026/08/05
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.