When I am reading Lunts' Categorical Resolution of Singularities, section 3.2, I found the following:
Let $A$ and $B$ be DG algebras and $N$ is a $A$-$B$-bimodule. Then we obtain a new DG algebra $$C=\begin{pmatrix}B&0\\N&A\end{pmatrix}$$
However, I cannot find the definition for this notation. So what is the new DG algebra, as well as its differential? Moreover, what is the motivation of this construction?
I find the DG-category version of the definition of gluing in the section 4 of Categorical resolutions of irrational singularities. If we treat the DG algebra as a DG-category with one object, the construction can be easily applied to DG algebras.