3 papers
math.KT2026
Anick Resolution for Lawvere Theories from Algebraic Discrete Morse Theory
Mirai Ikebuchi
Inspired by Brown's collapsing method (or discrete Morse theory) to obtain a free resolution of over the monoid ring , we apply algebraic discrete Morse theory to co…
math.CT2025
Cohomology of Small Cartesian Closed Categories
Mirai Ikebuchi
We show the isomorphism between the Quillen cohomology and the Baues-Wirsching cohomology of a cartesian closed category (CCC). This is an extension of the results of Dwyer-Kan for…
cs.LO2025
Homological Invariants of Higher-Order Equational Theories
Mirai Ikebuchi
Many first-order equational theories, such as the theory of groups or boolean algebras, can be presented by a smaller set of axioms than the original one. Recent studies showed tha…