My research aims at designing and implementing a well-defined, consistent, and usable category theory language for computer algebra systems.
CAP (Categories, Algorithms, Programming) is a software project for constructive category theory written in GAP. It facilitates both the realization of specific instances of categories and the implementation of generic categorical algorithms. With my colleague Sebastian Posur I gave an introduction at the Université Paris Diderot to constructive category theory and its applications to homological algebra.
The OSCAR project is meant to be the next generation computer algebra system, combining the power of the four computer algebra systems GAP, Nemo, polymake, and Singular by providing unlimited and full-speed access from and to those systems from julia. It will furthermore provide data structures and algorithms itself that combine functionaliy from all four systems.
|Constructive category theory and applications to algebraic geometry, PhD thesis, Siegen University.|
|Sebastian Gutche, Deciding kernel membership of the sheafification functor on toric varieties, MFO report no. 25 (2013).|