To complete a category is to embed it into a larger one which is closed under a given type of limits (or colimits). A fairly classical construction scheme, in which the objects of the new category are defined as "formal limits" of diagrams of the given one, is carried out in two specific examples. / In the case of the exact completion (')C of a finitely complete category C, we look at "formal coequalizers" of equivalence spans of C, which end up being the quotients (in (')C) of the corresponding equivalence relation. The objects of (')C are hence objects of C together with an equivalence span, and its morphisms are equivalence classes of "compatible" morphisms of C. Thus constructed, (')C is an exact category whose structure is studied in detail in Chapter I, as well as the universal property it satisfies. / The second example is the category pro-C of pro-objects, or "formal cofiltered limits" of C. Its objects are cofiltered diagrams of C, but can be characterized in various ways. The known properties of pro-C are summarized, extended and used to lift to pro-C some regularity and exactness properties of C (Chapters II & III). / The category of finite sets is an interesting example: its category of pro-objects is equivalent to the category of Stone spaces which is not exact, but whose exact completion in the sense of {9} is the category of compact Hausdorff spaces.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.71836 |
| Date | January 1983 |
| Creators | Meyer, Carol V. (Carol Vincent) |
| Publisher | McGill University |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Format | application/pdf |
| Coverage | Doctor of Philosophy (Department of Mathematics.) |
| Rights | All items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated. |
| Relation | alephsysno: 000167247, proquestno: AAINK64549, Theses scanned by UMI/ProQuest. |
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