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@article{1710256, author = {Bourke, John Denis}, article_number = {2}, keywords = {algebraic injective; globular theory; faithfulness conjecture}, language = {eng}, issn = {2209-0606}, journal = {Higher Structures}, title = {Iterated algebraic injectivity and the faithfulness conjecture}, url = {https://journals.mq.edu.au/index.php/higher_structures/article/view/120/81}, volume = {4}, year = {2020} }
TY - JOUR ID - 1710256 AU - Bourke, John Denis PY - 2020 TI - Iterated algebraic injectivity and the faithfulness conjecture JF - Higher Structures VL - 4 IS - 2 SP - 183-210 EP - 183-210 SN - 22090606 KW - algebraic injective KW - globular theory KW - faithfulness conjecture UR - https://journals.mq.edu.au/index.php/higher_structures/article/view/120/81 L2 - https://journals.mq.edu.au/index.php/higher_structures/article/view/120/81 N2 - 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. ER -
BOURKE, John Denis. Iterated algebraic injectivity and the faithfulness conjecture. \textit{Higher Structures}. 2020, roč.~4, č.~2, s.~183-210. ISSN~2209-0606.
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