  Ext groups are fundamental objects from homological algebra which underlie
important computations in homotopy theory. We formalise the theory of Yoneda
Ext groups in homotopy type theory (HoTT) using the Coq-HoTT library. This is
an approach to Ext which does not require projective or injective resolutions,
though it produces large abelian groups. Using univalence, we show how these
Ext groups can be naturally represented in HoTT. We give a novel proof and
formalisation of the usual six-term exact sequence via a fibre sequence of
1-types (or groupoids), along with an application. In addition, we discuss our
formalisation of the contravariant long exact sequence of Ext, an important
computational tool. Along the way we implement and explain the Baer sum of
extensions and how Ext is a bifunctor.
