# nLab Kleisli triple

Contents

### Context

#### Categorical algebra

internalization and categorical algebra

universal algebra

categorical semantics

# Contents

## Idea

Kleisli triple is the term chosen in Moggi (1991), Def. 1.2 for what was previously called an algebraic theory in extension form in Manes (1976), Ex. 3.12 (p. 32) and what later authors refer to as extension systems.

All of these terms refer to the equivalent axiomatization of monads (old terminology: “triples”) via the ingredients of their Kleisli categories under the Kleisli equivalence.

This is the natural and common incarnation of monads in computer science; see there for more.

## References

following

Created on November 5, 2022 at 13:27:03. See the history of this page for a list of all contributions to it.