2026-09-23T17:46:42Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/130097 2026-02-10 col_2142_5131 col_2142_16340 com_2142_5130 com_2142_16339 com_2142_8903

application/pdf en text Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2027-08-01 The student, Heyi Zhu, accepted the attached license on 2025-07-14 at 13:50. The student, Heyi Zhu, submitted this Dissertation for approval on 2025-07-14 at 14:08. This Dissertation was approved for publication on 2025-07-16 at 15:04. DSpace SAF Submission Ingestion Package generated from Vireo submission #22552 on 2025-10-25 at 15:30:59 A categorical approach to interactions between mod 2 power operations Zhu, Heyi 2025-07-16 Rezk, Charles W. Heller, Jeremiah Ben Stojanoska, Vesna Berwick-Evans, Daniel Algebraic Topology Primary Cohomology Operations In Algebraic Topology Dyer-lashof Operations eng We generalize the numerical formula due to Nishida which computes the effect of interchanging dual Steenrod operations and Dyer-Lashof operations acting on the homology of a space to a categorical relation between their A-based analogues over any given multiplicative cohomology theory A. Our approach interprets these two power operations as arising from comonadic and monadic structures on the homotopy category of A-modules. This perspective has the advantage of clearly identifying the computational input required to understand the interactions between these operations in concrete terms, given the choice of A—a feature not made explicit in previous work. 2025-08 Text https://hdl.handle.net/2142/130097 © 2025 Heyi Zhu All rights reserved. Mathematics Mathematics University of Illinois Urbana-Champaign Ph.D. Dissertation