A Logic of Injectivity

Details A Logic of Injectivity A Logic of Injectivity

2007-09-16

arxiv.org/abs/0709.2461v1

Mathematics

Category Theory

To be published in "Journal of Homotopy and Related Structures"

Scientific paper

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.

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