\chapter*{Abstract}
The usual notion of propositional equality in intensional type-theory is
restrictive. For instance it does not admit functional extensionality or
univalence. This poses a severe limitation on both what is \emph{provable} and
the \emph{re-usability} of proofs. Recent developments have, however, resulted
in cubical type theory which permits a constructive proof of these two important
notions. The programming language Agda has been extended with capabilities for
working in such a cubical setting. This thesis will explore the usefulness of
this extension in the context of category theory.

The thesis will motivate and explain why propositional equality in cubical Agda
is more expressive than in standard Agda. Alternative approaches to Cubical Agda
will be presented and their pros and cons will be explained. It will emphasize
why it is useful to have a constructive interpretation of univalence. As an
example of this two formulations of monads will be presented: Namely monaeds in
the monoidal form an monads in the Kleisli form.

Finally the thesis will explain the challenges that a developer will face when
working with cubical Agda and give some techniques to overcome these
difficulties. It will also try to suggest how furhter work can help allievate
some of these challenges.