Timeline for Cubical model category
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 31, 2018 at 14:32 | comment | added | Ronnie Brown | The book "Nonabelian Algebraic topology: filtered space, crossed complexes, cubical homotopy groupoids" (EMS, 2011) uses cubical methods which are essential for the main results, which give an accounts of the border between homology and homotopy theory without setting up singular homology theory. Cubes are better than simplices for discussing homotopies, and "algebraic inverses to subdivisions". | |
| Jun 30, 2016 at 19:51 | comment | added | Mike Shulman | There are many different things that "cubical set" can mean. Some of them do have a symmetric tensor product. | |
| Jun 30, 2016 at 17:13 | comment | added | Dmitri Pavlov | The general notion of an enriched model category specializes to the one you're looking for if one enriches over the model category of cubical sets (with or without connections). (It's not necessary for the monoidal structure on the enriching category to be symmetric.) The relevant theory also immediately implies that homotopy function spaces can be computed by deriving the enriched hom. | |
| Jun 29, 2016 at 18:55 | comment | added | Tyler Lawson | The category of cubical sets has the disadvantage that the monoidal product that you want is not the cartesian product, but a new one which is not symmetric. To my knowledge, most of the literature on enriched model categories assumes that the enriching category is symmetric. | |
| Jun 29, 2016 at 17:35 | history | asked | Philippe Gaucher | CC BY-SA 3.0 |