A Logic of Injectivity

  title={A Logic of Injectivity},
  author={Jir{\'i} Ad{\'a}mek and Michel H{\'e}bert and Leonel Sousa},
Injectivity of objects with respect to a set H of morphisms is an important concept of algebra and homotopy theory; here we study the logic of consequences of H, by which we understand morphisms h such that injectivity with respect to H implies injectivity with respect to h. We formulate three simple deduction rules for the injectivity logic and for its finitary version (where morphisms between finitely ranked objects are considered only), and prove that they are sound (in all categories) and… CONTINUE READING

From This Paper

Topics from this paper.


Publications citing this paper.


Publications referenced by this paper.
Showing 1-10 of 18 references

Homotopical Algebra, Lecture

  • D. Quillen
  • Notes Math. 43,
  • 1967
Highly Influential
3 Excerpts

A general axiomatizability theorem formulated in terms of coneinjective subcategories

  • H. Andréka, I. Németi
  • In : Universal Algebra ( Proc . Conf . Esztergom…
  • 2005

Logic of implications

  • J. Adámek, M. Sobral, L. Sousa
  • Preprints of the Department of Mathematics of the…
  • 2005
2 Excerpts

On a generalized small-object argument for the injective subcategory problem

  • J. Adámek, H. Herrlich, J. Rosický, W. Tholen
  • Cah. Topol. Géom. Différ. Catég. 43
  • 2002
1 Excerpt

Purity and injectivity in accessible categories

  • M. Hébert
  • J. Pure Appl. Algebra 129
  • 1998
1 Excerpt

Completeness of categorybased equational deduction , Mathem

  • F. Ulmer, Lokal Praesentierbare Kategorien
  • Comput . Sci .
  • 1995

Locally presentable and accessible categories

  • J. Adámek, J. Rosický
  • Cambridge University Press
  • 1994
1 Excerpt

Similar Papers

Loading similar papers…