Inspired by recent work of Peter O’Sullivan, we give a condition under which a faithful monoidal functor between abelian -categories is exact.
Revised:
Accepted:
Published online:
Mots-clés : Monoidal categories
Bruno Kahn 1

@article{CML_2022__14_2_45_0, author = {Bruno Kahn}, title = {Exactness and faithfulness of monoidal functors}, journal = {Confluentes Mathematici}, pages = {45--51}, publisher = {Institut Camille Jordan}, volume = {14}, number = {2}, year = {2022}, doi = {10.5802/cml.86}, language = {en}, url = {https://cml.centre-mersenne.org/articles/10.5802/cml.86/} }
Bruno Kahn. Exactness and faithfulness of monoidal functors. Confluentes Mathematici, Volume 14 (2022) no. 2, pp. 45-51. doi : 10.5802/cml.86. https://cml.centre-mersenne.org/articles/10.5802/cml.86/
[1] Y. André Slope filtrations, Confluentes Math. 1 (2009) 1–85. | DOI | MR | Zbl
[2] L. Barbieri-Viale, A. Huber, M. Prest Tensor structure for Nori motives, Pacific J. Math. 306, 2020, 1–30. | DOI | MR | Zbl
[3] K. Coulembier Additive Grothendieck pretopologies and presentations of tensor categories, preprint, 2020, . | arXiv
[4] K. Coulembier, P. Etingof, V. Ostrik, B. Pauwels Monoidal Abelian Envelopes with a quotient property, J. Reine Angew. Math. 794 (2023), 179 – 214. | Zbl
[5] P. Deligne, J. S. Milne Tannakian categories, in Hodge cycles, motives, and Shimura varieties, Lect. Notes in Math. 900, Springer, 1982, 101–228. | DOI
[6] P. Deligne Catégories tannakiennes, in The Grothendieck Festschrift, Vol. II, Progr. Math. 87, Birkhäuser, 1990, 111–195. | DOI
[7] P. Deligne Catégories tensorielles, Moscow Math. J. 2 (2002), 227–248. | DOI | MR | Zbl
[8] P. O’Sullivan Super Tannakian hulls, preprint (2020), . | arXiv
Cited by Sources: