## Archival Version

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A Logic of Injectivity
#
A Logic of Injectivity

##
J. Adamek, M. Hebert and L. Sousa

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.

Journal of Homotopy and Related Structures, Vol. 2(2007), No. 2, pp. 13-47