Abstract Levy

Many monads of interest can be characterized by universal properties, such as being a free monad or a coproduct or tensor of monads.   This talk is an overview of this active research area, drawing on universal algebra and programming language semantics.  We first establish the connection between universal and algebraic properties, leading to a range of examples.  Then we consider properties of monads on Set built in this way: injectivity of monad morphisms, universe independence, and convergence of transfinite constructions.

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