The idea of an operational category over A generalizes the notions of tripleable and equational category over A, and also the dual notions of cotripleable and coequational category. An operational category, U:D (--->) A is given by a presentation ((theta),H) (UNFORMATTED TABLE FOLLOWS) / D C('T) / C('(theta)) / A C('B) / H*(TABLE ENDS) / where (theta) is a functor bijective on objects and D is a specified pullback. R:Op(A) (--->) Cat/A is defined as the category of operational categories (and functors) with given presentations. Another category, Op(,o)(A) over Cat/A of operational categories with standard presentations is also defined. There is a fixed theory (theta)(,o), employed in every standard presentation. Op(,o)(A) is a retract of Op(A) over Cat/A: (UNFORMATTED TABLE FOLLOWS) / i / Op(,o)(A) Op(A) / s / R(,o) R / Cat/A(TABLE ENDS) / i.e. every operational category (and functor) has a standard presentation (but not s(REVTURNST)i!). Also R(,o) has a left adjoint L(,o) and Op(,o)(A) is complete. Finally, there is a category of algebras, S(,*)-Alg over Cat/A such that Op(,o)(A) (DBLTURN) S(,*)-Alg over Cat/A. Thus, the operational categories can be determined by their internal structure, without reference to any presentation. Some properties of operational categories and some special cases are also examined.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.71915 |
| Date | January 1984 |
| Creators | Jay, C. Barry. |
| 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 and Statistics.) |
| Rights | All items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated. |
| Relation | alephsysno: 000194969, proquestno: AAINK66657, Theses scanned by UMI/ProQuest. |
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