We introduce adhesive categories, which are categories with structure ensuring that pushouts along monomorphisms are well-behaved, as well as quasiadhesive categories which restrict attention to regular monomorphisms. Many examples of graphical structures used in computer science are shown to be examples of adhesive and quasiadhesive categories. Double-pushout graph rewriting generalizes well to rewriting on arbitrary adhesive and quasiadhesive categories.
Keywords: adhesive categories, quasiadhesive categories, extensive categories, category theory, graph rewriting
@article{ITA_2005__39_3_511_0,
author = {Lack, Stephen and Soboci\'nski, Pawe{\l}},
title = {Adhesive and quasiadhesive categories},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
pages = {511--545},
year = {2005},
publisher = {EDP Sciences},
volume = {39},
number = {3},
doi = {10.1051/ita:2005028},
zbl = {1078.18010},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ita:2005028/}
}
TY - JOUR AU - Lack, Stephen AU - Sobociński, Paweł TI - Adhesive and quasiadhesive categories JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2005 SP - 511 EP - 545 VL - 39 IS - 3 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/ita:2005028/ DO - 10.1051/ita:2005028 LA - en ID - ITA_2005__39_3_511_0 ER -
%0 Journal Article %A Lack, Stephen %A Sobociński, Paweł %T Adhesive and quasiadhesive categories %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2005 %P 511-545 %V 39 %N 3 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/ita:2005028/ %R 10.1051/ita:2005028 %G en %F ITA_2005__39_3_511_0
Lack, Stephen; Sobociński, Paweł. Adhesive and quasiadhesive categories. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 39 (2005) no. 3, pp. 511-545. doi: 10.1051/ita:2005028
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