Shahid Beheshti University Categories and General Algebraic Structures with Applications 2345-5853 24 1 2026 01 01 Replacing bar-like resolutions in a simplicial setting 137 150 105452 10.48308/cgasa.2024.235509.1488 EN Samuel Carolus Department of Defense, United States of America. Jacob Laubacher Department of Mathematics, St. Norbert College, De Pere, Wisconsin, United States of America. 0000-0003-0045-7951 Sydney D Vitalbo Department of Mathematics, St. Norbert College, De Pere, Wisconsin, United States of America. Leah K Widlarz Department of Mathematics, St. Norbert College, De Pere, Wisconsin, United States of America. Journal Article 2024 04 29 It is well known that the bar resolution can be replaced with any projective resolution of the corresponding algebra when computing the Hochschild (co)homology of that algebra. This is, in fact, a feature of its construction via derived functors. For generalizations and extensions of the Hochschild (co)homology (like the secondary and tertiary Hochschild (co)homology theory, as well as higher order Hochschild (co)homology theory), one uses a bar-like resolution in a simplicial setting within its construction in order to accommodate the changing module structures in every dimension. In this note, we present a method in order to replace these bar-like resolutions. https://cgasa.sbu.ac.ir/article_105452_c36d97390a7f025c98d5b1a13740d009.pdf