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Abstract
Our first aim is to provide an analog of the Gabriel-Quillen embedding theorem for n-exact categories. Also we give an example of an n-exact category that in not an n-cluster tilting subcategory, and we suggest two possible ways for realizing n-exact categories as n-cluster tilting subcategory.
Acknowledgment
Special thanks are due to the referee who read this paper carefully and made useful comments and suggestions that improved the presentation of the paper.
Additional information
Funding
This research was in part supported by a grant from IPM (No. 1400180047).