Cancellation theorems for reciprocity sheaves

Abstract

We prove cancellation theorems for reciprocity sheaves and cube-invariant modulus sheaves with transfers of Kahn--Saito--Yamazaki, generalizing Voevodsky's cancellation theorem for $\mathbf{A}^1$-invariant sheaves with transfers. As an application, we get some new formulas for internal hom's of the sheaves $\Omega^i$ of absolute K\"ahler differentials.