LAUSR

Let A be an abelian category and P(A) be the subcategory of A consisting of projective objects. Let C be a full, additive and self-orthogonal subcategory of A with P(A) a generator, and let G(C) be the Gorenstein subcategory of A. Then the right 1-orthogonal category $$G{(L)^{{ \bot _1}}}$$G(L)⊥1 of G(C) is both projectively resolving and injectively coresolving in A. We also get that the subcategory SPC(G(C)) of A consisting of objects admitting special G(C)-precovers is closed under extensions and C-stable direct summands (*). Furthermore, if C is a generator for $$G{(L)^{{ \bot _1}}}$$G(L)⊥1, then we have that SPC(G(C)) is the minimal subcategory of A containing $$G{(L)^{{ \bot _1}}}$$G(L)⊥1 ∪ G(C) with respect to the property (*), and that SPC(G(C)) is C-resolving in A with a C-proper generator C.