EMIS/ELibM Electronic Journals

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These pages are not updated anymore. They reflect the state of 6 June 2010. For the current production of this journal, please refer to http://www.springer.com/mathematics/geometry/journal/40062.

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