PreprintCC BY 4.0arXiv
On the natural transformations of extension functors
Abstract
Assume that n is a non-negative integer and C an n-Frobenius category. This paper is concerned with the natural transformations between extension functors on C. The main result of the paper indicates that for any pair of objects M, N∈ C, the group of all natural transformations from Extn+1C(N, −) to Extn+1C(M, −) is isomorphic to the quotient group ExtnC(M, syznN)/p, where p is the subgroup consisting of those Yoneda extensions of length n arising as a push-out along a morphism PrtsyznN, with P n-projective. This result is fruitful from the point of view that, n-Frobenius categories may not have projective objects.
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BibTeX
@misc{bahlekeh2026natural,
title = {{On the natural transformations of extension functors}},
author = {Abdolnaser Bahlekeh and Shokrollah Salarian},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.23495},
eprint = {2607.23495},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.23495},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On the natural transformations of extension functors
AU - Abdolnaser Bahlekeh
AU - Shokrollah Salarian
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2607.23495
UR - https://arxiv.org/abs/2607.23495
AB - Assume that n is a non-negative integer and C an n-Frobenius category. This paper is concerned with the natural transformations between extension functors on C. The main result of the paper indicates that for any pair of objects M, N∈ C, the group of all natural transformations from Ext^n+1_C(N, −) to Ext^n+1_C(M, −) is isomorphic to the quotient group Ext^n_C(M, syz^nN)/p, where p is the subgroup consisting of those Yoneda extensions of length n arising as a push-out along a morphism Prtsyz^nN, with P n-projective. This result is fruitful from the point of view that, n-Frobenius categories may not have projective objects.
ER -