The concept of a functor category provides one of the most important and useful methods for constructing new categories from given ones. Important special cases are the arrow category (morphism category) of a category, and the triangle category of a category. There is a non-trivial body of results known linking properties of the categories C (a small category) and D (an arbitrary category) to properties of the
associated functor category [C, D]. The project aims at a self-contained presentation of these results, including relevant background definitions and results, starting from the notions of categories, functors, and natural transformations. Full proofs of the main results are expected.
The relevant portions of the texts [1,2] should provide a good start and background for working on this project. Ambitious students, taking a deep interest in this topic, might then perhaps go further by conducting a literature search for more recent results on functor categories, and include some of their findings, if suitable within the framework of their thesis, as well (this part is optional and it is not clear where it might lead).
- H. Herrlich, G. E. Strecker, Category Theory. Allyn and Bacon Inc., Boston, 1973.
- H. Schubert, Categories. Springer-Verlag, Berlin-Heidelberg, 1972.
