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arXiv · 0709.2461

A Logic of Injectivity

J. Adamek·M. Hebert·L. Souza
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Abstract

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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J. Adamek, M. Hebert, L. Souza. 2007-09-16. A Logic of Injectivity. https://arxiv.org/abs/0709.2461

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