Contents

# Contents

## Idea

Given a modal operator $\bigcirc$, then a type $X$ may be called $\bigcirc$-comodal or $\bigcirc$-connected (largely now the preferred term) if $\bigcirc X \simeq \ast$ (the unit type).

Since a type $Y$ is called a $\bigcirc$-modal type if $\bigcirc Y \simeq Y$, being comodal is in a sense the opposite extreme of being modal.

In as far as modal operators have categorical semantics as idempotent (co-)-monads/idempotent (∞,1)-(co-)monads anti-modal types are familiar in homotopy theory as forming localizing subcategories.

## References

The term “anti-modal type” appears in

Last revised on March 25, 2020 at 06:27:58. See the history of this page for a list of all contributions to it.