On n -exact categories

Said Manjra

Czechoslovak Mathematical Journal (2019)

  • Volume: 69, Issue: 4, page 1089-1099
  • ISSN: 0011-4642

Abstract

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An n -exact category is a pair consisting of an additive category and a class of sequences with n + 2 terms satisfying certain axioms. We introduce n -weakly idempotent complete categories. Then we prove that an additive n -weakly idempotent complete category together with the class 𝒞 n of all contractible sequences with n + 2 terms is an n -exact category. Some properties of the class 𝒞 n are also discussed.

How to cite

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Manjra, Said. "On $n$-exact categories." Czechoslovak Mathematical Journal 69.4 (2019): 1089-1099. <http://eudml.org/doc/294517>.

@article{Manjra2019,
abstract = {An $n$-exact category is a pair consisting of an additive category and a class of sequences with $n+2$ terms satisfying certain axioms. We introduce $n$-weakly idempotent complete categories. Then we prove that an additive $n$-weakly idempotent complete category together with the class $\mathcal \{C\}_n$ of all contractible sequences with $n+2$ terms is an $n$-exact category. Some properties of the class $\mathcal \{C\}_n$ are also discussed.},
author = {Manjra, Said},
journal = {Czechoslovak Mathematical Journal},
keywords = {$n$-exact category; contractible sequence; idempotent complete category},
language = {eng},
number = {4},
pages = {1089-1099},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On $n$-exact categories},
url = {http://eudml.org/doc/294517},
volume = {69},
year = {2019},
}

TY - JOUR
AU - Manjra, Said
TI - On $n$-exact categories
JO - Czechoslovak Mathematical Journal
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 69
IS - 4
SP - 1089
EP - 1099
AB - An $n$-exact category is a pair consisting of an additive category and a class of sequences with $n+2$ terms satisfying certain axioms. We introduce $n$-weakly idempotent complete categories. Then we prove that an additive $n$-weakly idempotent complete category together with the class $\mathcal {C}_n$ of all contractible sequences with $n+2$ terms is an $n$-exact category. Some properties of the class $\mathcal {C}_n$ are also discussed.
LA - eng
KW - $n$-exact category; contractible sequence; idempotent complete category
UR - http://eudml.org/doc/294517
ER -

References

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  1. Borceux, F., 10.1017/CBO9780511525865, Encyclopedia of Mathematics and Its Applications, 50, Cambridge University Press, Cambridge (2008). (2008) Zbl1143.18002MR1313497DOI10.1017/CBO9780511525865
  2. Bühler, T., 10.1016/j.exmath.2009.04.004, Expo. Math. 28 (2010), 1-69. (2010) Zbl1192.18007MR2606234DOI10.1016/j.exmath.2009.04.004
  3. Freyd, P., 10.1007/978-3-642-99902-4_6, Proc. Conf. Categor. Algebra, La Jolla 1965 S. Eilenberg et al. Springer, Berlin (1966), 173-176. (1966) Zbl0195.52902MR0206069DOI10.1007/978-3-642-99902-4_6
  4. Geiss, C., Keller, B., Oppermann, S., 10.1515/crelle.2011.177, J. Reine Angew. Math. 675 (2013), 101-120. (2013) Zbl1271.18013MR3021448DOI10.1515/crelle.2011.177
  5. Iyama, O., 10.1016/j.aim.2006.06.003, Adv. Math. 210 (2007), 51-82. (2007) Zbl1115.16006MR2298820DOI10.1016/j.aim.2006.06.003
  6. Iyama, O., 10.1016/j.aim.2006.06.002, Adv. Math. 210 (2007), 22-50. (2007) Zbl1115.16005MR2298819DOI10.1016/j.aim.2006.06.002
  7. Iyama, O., 10.1016/j.aim.2010.03.004, Adv. Math. 226 (2011), 1-61. (2011) Zbl1233.16014MR2735750DOI10.1016/j.aim.2010.03.004
  8. Iyama, O., Yoshino, Y., 10.1007/s00222-007-0096-4, Invent. Math. 172 (2008), 117-168. (2008) Zbl1140.18007MR2385669DOI10.1007/s00222-007-0096-4
  9. Jasso, G., 10.1007/s00209-016-1619-8, Math. Z. 283 (2016), 703-759. (2016) Zbl1356.18005MR3519980DOI10.1007/s00209-016-1619-8
  10. Lin, Z., 10.1080/00927872.2016.1175591, Commun. Algebra 45 (2017), 828-840. (2017) Zbl1371.18010MR3562541DOI10.1080/00927872.2016.1175591
  11. Neeman, A., 10.1016/0021-8693(90)90296-z, J. Algebra 135 (1990), 388-394. (1990) Zbl0753.18004MR1080854DOI10.1016/0021-8693(90)90296-z
  12. Quillen, D., 10.1007/bfb0067053, Algebraic -Theory I: Higher -theories H. Bass Lecture Notes in Mathematics 341, Springer, Berlin (1973), 85-147. (1973) Zbl0292.18004MR0338129DOI10.1007/bfb0067053
  13. Thomason, R. W., Trobaugh, T., 10.1007/978-0-8176-4576-2_10, The Grothendieck Festschrift, Vol. III P. Cartier et al. Progress in Mathematics 88, Birkhäuser, Boston (1990), 247-435. (1990) Zbl0731.14001MR1106918DOI10.1007/978-0-8176-4576-2_10

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