Split objects with respect to a fully invariant short exact sequence in abelian categories
Rendiconti del Seminario Matematico della Università di Padova, Tome 147 (2022), pp. 1-41.
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We introduce and investigate (dual) relative split objects with respect to a fully invariant short exact sequence in abelian categories. We compare them with (dual) relative Rickart objects, and we study their behaviour with respect to coproducts and classes all of whose objects are (dual) relative split. We also introduce and study (dual) strongly relative split objects. Applications are given to Grothendieck categories, module categories, and comodule categories.

Publié le :
DOI : 10.4171/rsmup/88
Classification : 18, 16 
@article{RSMUP_2022__147__1_0,
     author = {Septimiu Crivei and Derya Keskin T\"ut\"unc\"u and Rachid Tribak},
     title = {Split objects with respect to a fully invariant short exact sequence in abelian categories},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {1--41},
     volume = {147},
     year = {2022},
     doi = {10.4171/rsmup/88},
     mrnumber = {4450782},
     zbl = {1497.18009},
     language = {en},
     url = {http://www.numdam.org/articles/10.4171/rsmup/88/}
}
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Septimiu Crivei; Derya Keskin Tütüncü; Rachid Tribak. Split objects with respect to a fully invariant short exact sequence in abelian categories. Rendiconti del Seminario Matematico della Università di Padova, Tome 147 (2022), pp. 1-41. doi : 10.4171/rsmup/88. http://www.numdam.org/articles/10.4171/rsmup/88/

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