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Homotopy in Functor Categories
| Content Provider | Scilit |
|---|---|
| Author | Heller, Alex |
| Copyright Year | 1982 |
| Description | If ${\mathbf {C}}$ is a small category enriched over topological spaces the category ${\mathcal {J}^{\mathbf {C}}}$ of continuous functors from ${\mathbf {C}}$ into topological spaces admits a family of homotopy theories associated with closed subcategories of ${\mathbf {C}}$. The categories ${\mathcal {J}^{\mathbf {C}}}$, for various ${\mathbf {C}}$, are connected to one another by a functor calculus analogous to the $\otimes$, Hom calculus for modules over rings. The functor calculus and the several homotopy theories may be articulated in such a way as to define an analogous functor calculus on the homotopy categories. Among the functors so described are homotopy limits and colimits and, more generally, homotopy Kan extensions. A by-product of the method is a generalization to functor categories of E. H. Brown's representability theorem. |
| Related Links | https://www.ams.org/tran/1982-272-01/S0002-9947-1982-0656485-2/S0002-9947-1982-0656485-2.pdf |
| Ending Page | 202 |
| Page Count | 18 |
| Starting Page | 185 |
| ISSN | 00029947 |
| e-ISSN | 10886850 |
| DOI | 10.2307/1998955 |
| Journal | Transactions of the American Mathematical Society |
| Issue Number | 1 |
| Volume Number | 272 |
| Language | English |
| Publisher | Duke University Press |
| Publisher Date | 1982-07-01 |
| Access Restriction | Open |
| Subject Keyword | Logic Mathematical Physics Functor Category |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics |
