On λ-pure exact structure

Document Type : Original Paper

Author

ِDepartment of mathematics shahid chamran university of ahvaz , ahvaz iran

Abstract

Let λ be an infinite regular cardinal and A be a locally λ-presentable additive category. It is shown that the class of all λ-pure short sequences in A induces an exact structure on A. Furthermore, we will show that any λ-pure short sequence is a λ-directed colimit of split sequences. In the case in which C is a class of objects in A which is closed under isomorphisms, we prove that C is closed under λ-directed colimits if and only if it is closed under λ-pure homomorphic images.

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Articles in Press, Accepted Manuscript
Available Online from 09 October 2024
  • Receive Date: 01 January 2024
  • Revise Date: 14 April 2024
  • Accept Date: 09 October 2024