1st Semester 2003/04: Categories of Interpretations
Relative interpretability is one of the most common ways of of comparing theories. E.g. `the Poincaré model' is a relative interpretation of two-dimensional hyperbolic geometry in two dimensional Eucidean geometry.
Surprisingly almost nothing is known about the category of interpretations. A moment of thought shows that there is in fact not one category of interpretations but that there are several depending on the answer to the question: when are two interpretations the same?
The project is to do some groundwork to settle some absolutely basic questions:
- Comparison of interpretations with or without parameters.
- Comparison of interpretations with or without relativization and with or without preservation of identity.
- Under what circumstances do sums exist? (I have a full answer for products.)
- What about equalizers and co-equalizers?
- Separating examples between the various categories.
- Classification of famous interpretations. E.g. is `the Poincaré model' a monomorphism?
- Should further structure be added to the categories to make them a fruitful tool to formulate classical results?
I will provide an introduction to the basic notions required to work on the project. Some knowledge of elementary category theory is helpful, but not strictly necessary.
- Location: The project will take place in Utrecht.