\chapter*{Abstract}
The usual notion of propositional equality in intensional type-theory
is restrictive. For instance it does not admit functional
extensionality nor 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 the need for univalence 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. As an example of
the application of univalence two formulations of monads will be
presented: Namely monads in the monoidal form and monads in the
Kleisli form and under the univalent interpretation it will be shown
how these are equal.

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 further
work can help alleviate some of these challenges.
