Contents

### Context

#### Categorical algebra

internalization and categorical algebra

universal algebra

categorical semantics

# Contents

## Idea

In computer science and specifically in type theory, a monad transformer is a type constructor which takes a monad as an argument and returns a monad as a result. The concept is typically treated in the literature on monads in computer science.

Monad transformers generally derive from ordinary monads and allow a modular composition, so that the action on the identity monad of the associated transform $M T$ of a monad $M$ is equivalent to $M$.

This construction is sometimes viewed (see HP07, Eff) as a complication resulting from passing to monads from the setting of Lawvere theories, where any two theories may be naturally combined.

## References

Textbook account: