# nLab inverse EI (∞,1)-category

Contents

### Context

#### $(\infty,1)$-Category theory

(∞,1)-category theory

# Contents

## Idea

An EI (∞,1)-category is an (∞,1)-category in which every endomorphism is an equivalence. This induces a ordering $\prec$ on the equivalence classes of objects, where x≺y means that there is a noninvertible morphism $y \to x$.

An inverse EI (∞,1)-category is an EI (∞,1)-category which is also an inverse (∞,1)-category, that is, is such that $\prec$ is well-founded, i.e., there are no infinite chains of noninvertible morphisms $\to \to \to \cdots$.

## References

Last revised on July 2, 2018 at 04:27:42. See the history of this page for a list of all contributions to it.