Recently, Oh-Thomas constructed a virtual cycle for a moduli space of stable sheaves on a Calabi-Yau 4-fold. In this talk, I will discuss how to localize the virtual cycle by an isotropic cosection and define a reduced virtual cycle when the cosection is surjective. Also, a vanishing result for a non-isotropic cosection will be discussed. I will explain how these results can be applied to various examples of cosections. This is joint work with Young-Hoon Kiem (arXiv:2012.13167).