nLab inverse EI (∞,1)-category

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 $\to \to \to \cdots$.

Examples

• For a compact Lie group $G$ the opposite of the orbit category.
• The category of finite sets and surjective functions.
• An EI (∞,1)-category with finitely many objects.

Related concepts

• poset-stratified space

References

• Mike Shulman, Univalence for inverse EI diagrams, (arXiv:1508.02410)