Given a finite-dimensional algebra $A$ over a field $k$, and a finite acyclic quiver $Q$, let $\Lambda = A\otimes_k kQ$, where $kQ$ is the path algebra of $Q$ over $k$. The monomorphism category ${\rm smon}(Q,A)$ was introduced around ten years ago. It turns out that this category is related with many mathematical branches, such as singularity theory, preprojective algebra, and plays an important role in relative homological algebra. In this talk, firstly, I will explain some results about the relation between monomorphism category and Gorenstein-projective modules which base on the cooperation with P. Zhang, W. Hu, B. Xiong, G. Zhou and T. Ju. Secondly, I will talk about the construction of separated monic representations basing on the paper joint with M. Schmidmeier.

会议密码:2022