The Cylinder of a Relation and Generalized Versions of the Nerve Theorem
We introduce the notion of cylinder of a relation in the context of posets, extending the construction of the mapping cylinder. We establish a local-to-global result for relations, generalizing Quillen’s Theorem A for order preserving maps, and derive novel formulations of the classical Nerve Theore...
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | INPR |
| Materias: | |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_01795376_v_n_p_Fernandez |
| Aporte de: |
| Sumario: | We introduce the notion of cylinder of a relation in the context of posets, extending the construction of the mapping cylinder. We establish a local-to-global result for relations, generalizing Quillen’s Theorem A for order preserving maps, and derive novel formulations of the classical Nerve Theorem for posets and simplicial complexes, suitable for covers with not necessarily contractible intersections. © 2018, Springer Science+Business Media, LLC, part of Springer Nature. |
|---|