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David Roberts ♦
David Roberts ♦
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These categories are called Puppe-exact or p-exact categories. See “Jordan-Hölder, modularity and distributivity in non-commutative algebra”, paragraph 1.1, byof Jordan-Hölder, modularity and distributivity in non-commutative algebra, by Francis Borceux and Marco Grandis (JPAA 208208 (2007), 665-689 ; available heredoi: http://www.dima.unige.it/~grandis/BGwe.Abs.html10.1016/j.jpaa.2006.03.004), for non-abelian examples. And see the papers of Marco Grandis (e.g. this one: http://www.numdam.org:80/numdam-bin/item?id=CTGDC_1992__33_2_135_0On the categorical foundations of homological and homotopical algebra (Numdam)) and Mitchell's book “Theory of categories” for homological results in this context (as a general rule, all homological lemmas non involving direct products hold).

These categories are called Puppe-exact or p-exact categories. See “Jordan-Hölder, modularity and distributivity in non-commutative algebra”, paragraph 1.1, by Francis Borceux and Marco Grandis (JPAA 208 (2007), 665-689 ; available here: http://www.dima.unige.it/~grandis/BGwe.Abs.html), for non-abelian examples. And see the papers of Marco Grandis (e.g. this one: http://www.numdam.org:80/numdam-bin/item?id=CTGDC_1992__33_2_135_0) and Mitchell's book “Theory of categories” for homological results in this context (as a general rule, all homological lemmas non involving direct products hold).

These categories are called Puppe-exact or p-exact categories. See paragraph 1.1, of Jordan-Hölder, modularity and distributivity in non-commutative algebra, by Francis Borceux and Marco Grandis (JPAA 208 (2007), 665-689 doi:10.1016/j.jpaa.2006.03.004), for non-abelian examples. And see the papers of Marco Grandis (e.g. On the categorical foundations of homological and homotopical algebra (Numdam)) and Mitchell's book “Theory of categories” for homological results in this context (as a general rule, all homological lemmas non involving direct products hold).

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Mathieu Breckes
Mathieu Breckes
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These categories are called Puppe-exact or p-exact categories. See “Jordan-Hölder, modularity and distributivity in non-commutative algebra”, paragraph 1.1, by Francis Borceux and Marco Grandis (JPAA 208 (2007), 665-689 ; available here: http://www.dima.unige.it/~grandis/BGwe.Abs.html), for non-abelian examples. And see the papers of Marco Grandis (e.g. this one: http://www.numdam.org:80/numdam-bin/item?id=CTGDC_1992__33_2_135_0) and Mitchell's book “Theory of categories” for homological results in this context (as a general rule, all homological lemmas non involving direct products hold).

These categories are called Puppe-exact or p-exact categories. See “Jordan-Hölder, modularity and distributivity in non-commutative algebra”, paragraph 1.1, by Francis Borceux and Marco Grandis (JPAA 208 (2007), 665-689 ; available here: http://www.dima.unige.it/~grandis/BGwe.Abs.html), for non-abelian examples. And see the papers of Marco Grandis (e.g. this one: http://www.numdam.org:80/numdam-bin/item?id=CTGDC_1992__33_2_135_0) for homological results in this context (as a general rule, all homological lemmas non involving direct products hold).

These categories are called Puppe-exact or p-exact categories. See “Jordan-Hölder, modularity and distributivity in non-commutative algebra”, paragraph 1.1, by Francis Borceux and Marco Grandis (JPAA 208 (2007), 665-689 ; available here: http://www.dima.unige.it/~grandis/BGwe.Abs.html), for non-abelian examples. And see the papers of Marco Grandis (e.g. this one: http://www.numdam.org:80/numdam-bin/item?id=CTGDC_1992__33_2_135_0) and Mitchell's book “Theory of categories” for homological results in this context (as a general rule, all homological lemmas non involving direct products hold).

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Mathieu Breckes
Mathieu Breckes
  • 136
  • 1
  • 4

These categories are called Puppe-exact or p-exact categories. See “Jordan-Hölder, modularity and distributivity in non-commutative algebra”, paragraph 1.1, by Francis Borceux and Marco Grandis (JPAA 208 (2007), 665-689 ; available here: http://www.dima.unige.it/~grandis/BGwe.Abs.html), for non-abelian examples. And see the papers of Marco Grandis (e.g. this one: http://www.numdam.org:80/numdam-bin/item?id=CTGDC_1992__33_2_135_0) for homological results in this context (as a general rule, all homological lemmas non involving direct products hold).