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nLab

negative moment

# Contents

## Idea

In the context of idempotent (∞,1)-monads or comonads, or *moments*, the **negative moment** is the homotopy fiber of the unit or homotopy cofiber of the counit.

These are denoted, e.g., $\overline{\sharp}$, $\overline{\flat}$.

- The negative of $id$ (both as monad and comonad) is $\ast$.
- The negative of $\ast$ is $id$.
- The negative of $\emptyset$ is the maybe monad, although not itself idempotent, so not a moment.