UC Riverside

The notion of an algebraic theory, which is able to describe many algebraic structures, has been used extensively since its

introduction by Lawvere in 1963. This perspective has been very fruitful for understanding in a wide variety of algebraic

structures, including rigidification results for simplicial algebras over algebraic theories by Badzioch and Bergner. In

this thesis, we extend the rigidification results to algebras over a larger class of categories, which includes bisimplicial

sets. In particular, we prove the rigidification result is true in any diagram category $\SSets^{\mathcal{C}^{op}}$ for a small category $\mathcal{C}$.