  We provide a generalization of the construction of a spectrum of a
commutative ring as a locally ringed space, applicable to cone injectivity
classes in general contexts, especially in locally finitely presentable
categories. In its full generality, the spectrum functor fails to be fully
faithful and we study reasonable sufficient conditions under which it is.
Further, assuming the full faithfulness, we introduce a generalization of
another concept from algebraic geometry -- the functor of points -- and prove
equivalence of the two resulting notions of schemes.
