Let C,D be categories, let F be a functor from C to D, and let G be right adjoint to F. In a recent paper of Connes and Consani, they consider the following "pasting along an adjunction": let E be a category whose object class is the union of the object class of C and the object class of D; and given objects X,Y of E, let the hom-set hom_E(X,Y) be defined as follows: -if X,Y are both in the object class of C, then hom_E(X,Y) = hom_C(X,Y). -if X,Y are both in the object class of D, then hom_E(X,Y) = hom_D(X,Y). -if X is in the object class of C and Y is in the object class of D, then hom_E(X,Y) = hom_C(X,GY) = hom_D(FX,Y). -if X is in the object class of D and Y is in the object class of C, then hom_E(X,Y) is empty. Composition is defined in a straightforward way. When C,D are closed symmetric monoidal categories, then E has a natural closed symmetric monoidal structure as well. Connes and Consani use this categorical pasting to construct schemes over F_1, "the field with one element," and I have worked out some variations and applications of this categorical pasting which produce other useful objects (e.g. algebraic F_1-stacks and derived F_1-stacks, which have some useful number-theoretic as well as homotopy-theoretic properties). I would like to know if this "pasting along an adjunction" is a special case of some more general construction already known to category theory, and if basic properties of pasting along an adjunction have already been worked out and written down somewhere. Thanks, Andrew S.