Higher Theories and Monads

Monads and algebraic theories are two categorical approach to universal algebra. In his book Higher Algebra, Jacob Lurie established a relatively comprehensive theory of monads on infinity categories. However, his approach can be difficult in practice to use due to its highly technical nature. In this talk, we will describe a version of generalized algebraic theories in the $\infty$-categorical setting, and show that it is recovers Lurie's theory for nice monads. As an application, we will prove several structural results about monads in the $\infty$-categorical setting. We will also use our result to describe the algebraic theories of E_1, E_2, and E_\infty algebras.