  Injectivity of objects with respect to a set $\ch$ of morphisms is an
important concept of algebra, model theory and homotopy theory. Here we study
the logic of injectivity consequences of $\ch$, by which we understand
morphisms $h$ such that injectivity with respect to $\ch$ implies injectivity
with respect to $h$. We formulate three simple deduction rules for the
injectivity logic and for its finitary version where \mor s between finitely
ranked objects are considered only, and prove that they are sound in all
categories, and complete in all "reasonable" categories.

Category Theory