  Let (S; n) be a commutative noetherian local ring and let w in n be non-zero
divisor. This paper is concerned with the two categories of monomorphisms
between finitely generated (Gorenstein) projective S-modules, such that their
cokernels are annihilated by w. It is shown that these categories, which will
be denoted by Mon(w;P) and Mon(w; G), are both Frobenius categories with the
same projective objects. It is also proved that the stable category Mon(w;P) is
triangle equivalent to the category of D-branes of type B, DB(w), which has
been introduced by Kontsevich and studied by Orlov. Moreover, it will be
observed that the stable categories Mon(w;P) and Mon(w; G) are closely related
to the singularity category of the factor ring R = S=(w). Precisely, there is a
fully faithful triangle functor from the stable category Mon(w; G) to Dsg(R),
which is dense if and only if R (and so S) are Gorenstein rings. Particularly,
it is proved that the density of the restriction of this functor to Mon(w;P),
guarantees the regularity of the ring S.
