nLab negative moment

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.

Related concepts

• differential cohomology hexagon
• extensive quantity