A -autonomous category is a symmetric monoidal closed category such that ...
Please expand, including both symmetric and non-symmetric versions, and short definition due to Ehrhard.
Melliès, Paul-André. 2009. ‘Categorical Semantics of Linear Logic’. In Panoramas et Synthèses 27: Interactive Models of Computation and Program Behaviour, edited by Pierre-Louis Curien, Hugo Herbelin, Jean-Louis Krivine, and Paul-André Melliès. Société Mathématique de France. [pdf]
@incollection{mellies_categorical_2009,
title = {Categorical {Semantics} of {Linear} {Logic}},
isbn = {978-2-85629-273-0},
url = {http://www.pps.univ-paris-diderot.fr/~mellies/papers/panorama.pdf},
booktitle = {Panoramas et synthèses 27: {Interactive} models of computation and program behaviour},
publisher = {Soci\'{e}t\'{e} Mathématique de France},
author = {Melliès, Paul-André},
editor = {Curien, Pierre-Louis and Herbelin, Hugo and Krivine, Jean-Louis and Melli\`{e}s, Paul-Andr\'{e}},
year = {2009}
}
Barr, Michael. 1991. ‘*-Autonomous Categories and Linear Logic’. Mathematical Structures in Computer Science 1 (2): 159–78. https://doi.org/10.1017/S0960129500001274.
@article{barr_1991,
title = {*-{Autonomous} categories and linear logic},
volume = {1},
issn = {14698072},
doi = {10.1017/S0960129500001274},
number = {2},
journal = {Mathematical Structures in Computer Science},
author = {Barr, Michael},
year = {1991},
pages = {159--178}
Barr, Michael. 1995. ‘Nonsymmetric ∗-Autonomous Categories’. Theoretical Computer Science 139: 115–30. https://doi.org/10.1016/0304-3975(94)00089-2.
@article{barr_1995,
title = {Nonsymmetric ∗-autonomous categories},
volume = {139},
doi = {10.1016/0304-3975(94)00089-2},
language = {en},
journal = {Theoretical Computer Science},
author = {Barr, Michael},
year = {1995},
pages = {115--130}
}