nLab
Grothendieck-Maltsiniotis infinity-category

Idea

An algebraic definition of ∞-groupoids and ∞-categories similar to (but older than) the definition Batanin ω-categories.

References

The original definition is indicated in words in sections 1-13 of

• Alexander Grothendieck, Pursuing Stacks

This has been extracted and formalized in

• Georges Maltsiniotis, Infini groupoïdes d’après Grothendieck (web)

A comprehensive account of a simplified version of the definition and its generalization from $\mathrm{\infty }$-groupoids to $\mathrm{\infty }$-categories is given in

• Georges Maltsiniotis, Grothendieck $\mathrm{\infty }$-groupoids and still another definition of $\mathrm{\infty }$-categories (arXiv:1009.2331)

The relation to Batanin ω-categories is discussed in

• Dimitri Ara, Sur les $\mathrm{\infty }$-groupoïdes de Grothendieck Thesis, under the supervision of G. Maltsiniotis, (2010) (pdf)

A brief survey is provided in

• Mike Shulman, (blog entry)