Let \(\mathcal {A}\) and \(\mathcal {B}\) be abelian categories and \({\mathbf {F}} :\mathcal {A}\rightarrow \mathcal {B}\) 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.

设\(\mathcal {A}\)和\(\mathcal {B}\)是阿贝尔范畴，而\({\mathbf {F}} :\mathcal {A}\rightarrow \mathcal {B}\)是加法和完美的右精确函子，让\(({\mathbf {F}},\mathcal {B})\)是左逗号类别。我们给出了\(({\mathbf {F}},\mathcal {B})\)中Gorenstein 射影对象的等效表征，即\(\mathcal {B}\)和\(\mathcal {A}\)。我们证明了\(({\mathbf {F}},\mathcal {B})\)由 Gorenstein 投影对象模投影组成，相对于\(\mathcal {B}\)和\(\mathcal {A}\) 中的同类稳定类别。此外，当\(\mathcal {B}\)是 Gorenstein 并且\({\mathbf {F}}\)保留射影时，这个左重排可以填充为重排。