Iterated algebraic injectivity and the faithfulness conjecture
| Authors | |
|---|---|
| Year of publication | 2020 |
| Type | Article in Periodical |
| Magazine / Source | Higher Structures |
| MU Faculty or unit | |
| Citation | |
| Web | https://journals.mq.edu.au/index.php/higher_structures/article/view/120/81 |
| Keywords | algebraic injective; globular theory; faithfulness conjecture |
| Description | Algebraic injectivity was introduced to capture homotopical structures like algebraic Kan complexes. But at a much simpler level, it allows one to describe sets with operations subject to no equations. If one wishes to add equations (or operations of greater complexity) then it is natural to consider iterated algebraic injectives, which we introduce and study in the present paper. Our main application concerns Grothendieck's weak omega-groupoids, introduced in Pursuing Stacks, and the closely related definition of weak omega-category due to Maltsiniotis. Using omega iterations we describe these as iterated algebraic injectives and, via this correspondence, prove the faithfulness conjecture of Maltsiniotis. Through work of Ara, this implies a tight correspondence between the weak omega-categories of Maltsiniotis and those of Batanin/Leinster. |
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