Ultraproducts and continuous families of models.
| dc.contributor.author | Marmolejo, Francisco. | en_US |
| dc.contributor.degree | Ph.D. | en_US |
| dc.date.accessioned | 2014-10-21T12:37:15Z | |
| dc.date.available | 1995 | |
| dc.date.issued | 1995 | en_US |
| dc.description | Let P be a small pretopos. Makkai showed that the pretopos (i.e. the language) can be recovered from the category of models of the pretopos (i.e. Set-valued functors preserving the pretopos structure). The realization that ultraproduct functors can be expressed as composition of functors on categories of sheaves over topological spaces opens the door for using continuous families of models, that is, categories indexed topological spaces. | en_US |
| dc.description | We introduce a special kind of category indexed over topological spaces in which it is possible to define ultraproduct functors. This involves continuous functions $f:Y\to X$ for which the functors $f\sb{*}:Sh(Y)\to Sh(X)$ preserve the pretopos structure. We give a characterization of such functions. Each of these indexed categories produces a pre-ultracategory in the sense of Makkai. | en_US |
| dc.description | We also consider the 2-adjunction $PRETOP\sp{op}\sbsp{Mod\sp{(\sb-)}}{Set\sp{(\sb-)}}CAT$ and the 2-monad it generates. We show that each algebra for this 2-monad carries a pre-ultracategory structure as well. We induce another 2-monad over the category of algebras and show that these new algebras carry the structure of ultracategories. | en_US |
| dc.description | We combine both approaches by defining a 2-adjunction over the 2-category of special indexed categories mentioned above and show that the corresponding algebras also carry ultracategory structures. | en_US |
| dc.description | Finally, aiming at giving filtered colimits a bigger role in the picture we generalize a theorem of Lever, namely, that indexed functors from the indexed category that has the category of sheaves $Sh(X)$ over the topological space X, to itself is equivalent to the category of filtered colimit preserving functors from Set to itself. | en_US |
| dc.description | Thesis (Ph.D.)--Dalhousie University (Canada), 1995. | en_US |
| dc.identifier.other | AAINN08788 | en_US |
| dc.identifier.uri | http://hdl.handle.net/10222/55092 | |
| dc.language | eng | en_US |
| dc.publisher | Dalhousie University | en_US |
| dc.publisher | en_US | |
| dc.subject | Mathematics. | en_US |
| dc.title | Ultraproducts and continuous families of models. | en_US |
| dc.type | text | en_US |
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