Let $\mathcal{ A}$ and $\mathcal{ B}$ be abelian categories and $\mathbf{ F}:\mathcal{ A}\to \mathcal{ B}$ an additive and right exact functor which is perfect, and let $(\mathbf{ F},\mathcal{ B})$ be the left comma category. We give an equivalent characterization of Gorenstein projective objects in $(\mathbf{ F},\mathcal{ B})$ in terms of Gorenstein projective objects in $\mathcal{ B}$ and $\mathcal{ A}$. We prove that there exists a left recollement of the stable category of the subcategory of $(\mathbf{ F},\mathcal{ B})$ consisting of Gorenstein projective objects modulo projectives relative to the same kind of stable categories in $\mathcal{ B}$ and $\mathcal{ A}$. Moreover, this left recollement can be filled into a recollement when $\mathcal{ B}$ is Gorenstein and $\mathbf{ F}$ preserves projectives.
Categories: math.RA