Templates and worlds for interpretations [microform]
- Bib ID:
- 3283613
- Format:
- Book and Microform
- Author:
- Ensor, Andrew James
- Description:
- 52 p.
- Summary:
-
A template is a graph that has been enriched by the addition of distinguished cones and/or cocones. Different templates give various contexts for the mathematics, such as group theory, category theory, or some variety of general algebras. A world is a graph that represents a particular mathematical notion. Notions such as structure, morphism, or formation can each be given by an appropriate world. A graph map from a template into a world that takes the distinguished cones and cocones of the template and maps them to limits and colimits respectively in the world is called an interpretation of the template in the world. An interpretation gives a representation of the notion determined by the world in the context of the theory dictated by the template. In this thesis, templates are described that provide the context for some familiar theories of mathematics. Then, a system of worlds is defined, and interpretations of some templates in these worlds are investigated in detail.
Ideas which are shown to be representable by interpretations include algebras, categories, homomorphisms, functors, natural transformations, and adjunctions. The motivation and power of this work is demonstrated by the ability to create worlds that allow many notions of mathematics to be representable by interpretations. Then, using different templates these notions can be shifted to other areas of mathematics, sometimes with some interesting consequences.
- Notes:
-
- (UnM)AAI9621127
- Source: Dissertation Abstracts International, Volume: 57-03, Section: B, page: 1841.
- Chair: Ralph McKenzie.
- Thesis (Ph.D.)--University of California, Berkeley, 1995.
- Reproduction:
- Microfiche. Ann Arbor, Mich.: University Microfilms International.
- Subject:
- Mathematics
- Other authors/contributors:
- University of California, Berkeley
- Copyright:
-
In Copyright
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Copyright status was determined using the following information:
- Material type:
- Literary Dramatic Musical
- Published status:
- Unpublished
- Creation date:
- 1995
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