Idempotence for relative monads

TL;DR

This paper explores the concept of idempotence in relative monads, revealing subtleties and bifurcations not seen in traditional monads, and provides characterizations for monads in extension form.

Contribution

It introduces a nuanced analysis of idempotence in relative monads, including bifurcations and characterizations specific to extension form monads.

Findings

Identifies multiple notions of idempotence in relative monads

Shows bifurcation phenomena not present in non-relative monads

Provides characterizations for idempotence in extension form monads

Abstract

We study the concept of idempotence for relative monads, which exhibits several subtleties not present for non-relative monads. In particular, there is a bifurcation of notions of idempotence in the relative setting, which are indistinguishable for idempotent monads. As a special case, we obtain several characterisations of idempotence for monads in extension form.