An axiomatic construction of an almost full embedding of the category of graphs into the category of -objects
| ISSN: | 0022-4049 |
|---|---|
| Přístupová URL adresa: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1719e7e04bba1c5219f22bca954bf4f7 https://doi.org/10.1016/j.jpaa.2013.05.006 |
| Rights: | OPEN |
| Přírůstkové číslo: | edsair.doi.dedup.....1719e7e04bba1c5219f22bca954bf4f7 |
| Autor: | Adam J. Przeździecki, Rüdiger Göbel |
| Rok vydání: | 2014 |
| Předmět: |
Discrete mathematics
Algebra and Number Theory Complete category Concrete category Category of groups Mathematics - Category Theory Mathematics - Rings and Algebras Mathematics - Commutative Algebra Commutative Algebra (math.AC) Combinatorics Category of rings Rings and Algebras (math.RA) Mathematics::Category Theory Mathematik Category FOS: Mathematics 18B15 13C05 13C10 13C13 20K20 20K25 20K30 Category of topological spaces Category Theory (math.CT) Biproduct Category of sets Mathematics |
| Zdroj: | Journal of Pure and Applied Algebra. 218:208-217 |
| ISSN: | 0022-4049 |
| Popis: | We construct embeddings G of the category of graphs into categories of R-modules over a commutative ring R which are almost full in the sense that the maps induced by the functoriality of G R[Hom_Graphs(X,Y)] --> Hom_R(GX,GY) are isomorphisms. The symbol R[S] above denotes the free R-module with the basis S. This implies that, for any cotorsion-free ring R, the categories of R-modules are not less complicated than the category of graphs. A similar embedding of graphs into the category of vector spaces with four distinguished subspaces (over any field, e.g. F_2={0,1} is obtained). 20 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect