Injectivity of objects with respect to a set H of morphisms is an important concept of algebra and homotopy theory; here we study the logic of consequences of H, by which we understand morphisms h such that injectivity with respect to H implies injectivity with respect to h. We formulate three simple deduction rules for the injectivity logic and for its finitary version (where morphisms between finitely ranked objects are considered only), and prove that they are sound (in all categories) and… CONTINUE READING