Abstract

UniMath refers to several things. It is a
univalent foundation of mathematics. It is the subset of Coq in which this
foundation is currently implemented and it is a library of formalized
mathematics written using this implementation. My talk will be mostly about the
library. I will give examples of problems whose constructions have been
recently formalized in the UniMath as study problems by graduate students. I
will give an example of a more complex problem whose construction has been
recently formalized as a part of a paper accepted to a conference proceedings.
Finally, I will outline a direction for the future development of the UniMath
that requires constructions to considerably more complex problems that can only
be stated in the univalent type theory and, as far as I know, have never been
solved either formally or informally.