Abstract
This note provides an elementary short proof of the known fact that the category \(\mathfrak {F} \left( \Delta \right) \) of \(\Delta \)-filtered modules, associated to a given finite homological system \(\left( \Delta ; \Omega , \le \right) ,\) is closed under direct summands.
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References
Mendoza, O., Sáenz, C., Xi, C.: Homological systems in module categories over pre-ordered sets. Q. J. Math. 60, 75–103 (2009)
Ringel, C.M.: The category of \(\Delta \)-good modules over a quasi-hereditary algebra has almost split sequences. Math. Z. 208, 209–223 (1991)
Acknowledgements
Thanks to the referee for nice suggestions and comments, and to Raymundo Bautista and Leonardo Salmerón for a great introduction to quasi-hereditary algebras.
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Pérez Terrazas, J.E. A note on homological systems. Arch. Math. 117, 631–634 (2021). https://doi.org/10.1007/s00013-021-01648-3
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DOI: https://doi.org/10.1007/s00013-021-01648-3