  We present our library for Universal Algebra in the UniMath framework dealing
with multi-sorted signatures, their algebras, and the basics for equation
systems. We show how to implement term algebras over a signature without
resorting to general inductive constructions (currently not allowed in UniMath)
still retaining the computational nature of the definition. We prove that our
single sorted ground term algebras are instances of homotopy W-types. From this
perspective, the library enriches UniMath with a computationally well-behaved
implementation of a class of W-types. Moreover, we give neat constructions of
the univalent categories of algebras and equational algebras by using the
formalism of displayed categories, and show that the term algebra over a
signature is the initial object of the category of algebras. Finally, we
showcase the computational relevance of our work by sketching some basic
examples from algebra and propositional logic.
