@article(abrusci:noncommutative:1990, author = {V. Michele Abrusci}, year = {1990}, title = {Non-commutative Intuitionistic Linear Logic}, journal = {Mathematical Logic Quarterly}, volume = {36}, number = {4}, pages = {297--318}, doi = {10.1002/malq.19900360405}, ) @article(altenkirch:monads:2014, author = {Thorsten Altenkirch and James Chapman and Tarmo Uustalu}, year = {2015}, title = {Monads Need Not Be Endofunctors}, journal = {Logical Methods in Computer Science}, volume = {11}, number = {1}, eid = {3}, doi = {10.2168/lmcs-11(1:3)2015}, ) @article(andreoli:logic:1992, author = {Jean-Marc Andreoli}, year = {1992}, title = {Logic Programming with Focusing Proofs in Linear Logic}, journal = {Journal of Logic and Computation}, volume = {2}, number = {3}, pages = {297--347}, doi = {10.1093/logcom/2.3.297}, ) @article(bourke:skew:2017, author = {John Bourke}, year = {2017}, title = {Skew structures in 2-category theory and homotopy theory}, journal = {Journal of Homotopy and Related Structures}, volume = {12}, number = {1}, pages = {31--81}, doi = {10.1007/s40062-015-0121-z}, ) @article(bourke:skew:2018, author = {John Bourke and Stephen Lack}, year = {2018}, title = {Skew Monoidal Categories and Skew Multicategories}, journal = {Journal of Algebra}, volume = {506}, pages = {237--266}, doi = {10.1016/j.jalgebra.2018.02.039}, ) @article(buckley:catalan:2015, author = {Michael Buckley and Richard Garner and Stephen Lack and Ross Street}, year = {2015}, title = {The {C}atalan Simplicial Set}, journal = {Mathematical Proceedings of Cambridge Philosophical Society}, volume = {158}, number = {2}, pages = {211--222}, doi = {10.1017/s0305004114000498}, ) @inproceedings(chaudhuri:canonical:2008, author = {Kaustuv Chaudhuri and Dale Miller and Alexis Saurin}, year = {2008}, title = {Canonical Sequent Proofs via Multi-Focusing}, editor = {Giorgio Ausiello and Juhani Karhum{\"{a}}ki and Giancarlo Mauri and Luke Ong}, booktitle = {Proceedings of 5th IFIP International Conference on Theoretical Computer Science, {TCS} 2008}, series = {International Federation of Information Processing Series}, volume = {273}, publisher = {Springer}, pages = {383--396}, doi = {10.1007/978-0-387-09680-3\_26}, ) @incollection(dyckhoff:ljq, author = {Roy Dyckhoff and St{\'e}phane Lengrand}, year = {2006}, title = {LJQ: A Strongly Focused Calculus for Intuitionistic Logic}, editor = {Arnold Beckmann and Ulrich Berger and Benedikt L{\"o}we and John V. Tucker}, booktitle = {Proceedings of the 2nd Conference on Computability in Europe, CiE 2006}, series = {Lecture Notes in Computer Science}, volume = {3988}, publisher = {Springer}, pages = {173--185}, doi = {10.1007/11780342_19}, ) @inproceedings(eilenberg:closed:1966, author = {Samuel Eilenberg and G. Max Kelly}, year = {1966}, title = {Closed Categories}, editor = {Samuel Eilenberg and David K. Harrison and {Mac Lane}, Saunders and Helmut R\"ohrl}, booktitle = {Proceedings of the Conference on Categorical Algebra (La Jolla, 1965)}, publisher = {Springer}, pages = {421--562}, doi = {10.1007/978-3-642-99902-4\_22}, ) @article(girard:constructive:91, author = {Jean-Yves Girard}, year = {1991}, title = {A New Constructive Logic: Classical Logic}, journal = {Mathematical Structures in Computer Science}, volume = {1}, number = {3}, pages = {255--296}, doi = {10.1017/s0960129500001328}, ) @inproceedings(hasegawa:linear:2017, author = {Masahito Hasegawa}, year = {2016}, title = {Linear Exponential Comonads without Symmetry}, editor = {Iliano Cervesato and Maribel Fern{\'{a}}ndez}, booktitle = {Proceedings of the 4th International Workshop on Linearity, {LINEARITY} 2016}, series = {Electronic Proceedings in Theoretical Computer Science}, volume = {238}, publisher = {Open Publishing Association}, pages = {54--63}, doi = {10.4204/etpcs.238.6}, ) @inproceedings(jiang:lambek:2019, author = {Jiaming Jiang and {Eades III}, Harley and {de Paiva}, Valeria}, year = {2018}, title = {On the {L}ambek Calculus with an Exchange Modality}, editor = {Thomas Ehrhard and Maribel Fern{\'{a}}ndez and {de Paiva}, Valeria and {Tortora de Falco}, Lorenzo}, booktitle = {Proceedings of the Joint International Workshop on Linearity {\&} Trends in Linear Logic and Applications, Linearity-TLLA 2018}, series = {Electronic Proceedings in Theoretical Computer Science}, volume = {292}, publisher = {Open Publishing Association}, pages = {43--89}, doi = {10.4204/eptcs.292.4}, ) @article(lack:skew:2012, author = {Stephen Lack and Ross Street}, year = {2012}, title = {Skew Monoidales, Skew Warpings and Quantum Categories}, journal = {Theory and Applications of Categories}, volume = {26}, pages = {385--402}, url = {http://www.tac.mta.ca/tac/volumes/26/15/26-15abs.html}, ) @article(lack:triangulations:2014, author = {Stephen Lack and Ross Street}, year = {2014}, title = {Triangulations, Orientals, and Skew Monoidal Categories}, journal = {Advances in Mathematics}, volume = {258}, pages = {351--396}, doi = {10.1016/j.aim.2014.03.003}, ) @article(lambek:mathematics:58, author = {Joachim Lambek}, year = {1958}, title = {The Mathematics of Sentence Structure}, journal = {American Mathematical Monthly}, volume = {65}, number = {3}, pages = {154--170}, doi = {10.2307/2310058}, ) @article(lambek:deductive:68, author = {Joachim Lambek}, year = {1968}, title = {Deductive Systems and Categories {I}: Syntactic Calculus and Residuated Categories}, journal = {Mathematical Systems Theory}, volume = {2}, number = {4}, pages = {287--318}, doi = {10.1007/bf01703261}, ) @article(maclane1963natural, author = {{Mac Lane}, Saunders}, year = {1963}, title = {Natural Associativity and Commutativity}, journal = {Rice University Studies}, volume = {49}, number = {4}, pages = {28--46}, url = {http://hdl.handle.net/1911/62865}, ) @incollection(mellies:categorical:09, author = {Paul-Andr{\'e} Melli{\`e}s}, year = {2009}, title = {Categorical Semantics of Linear Logic}, editor = {Pierre-Louis Curien and Hugo Herbelin and Jean-Louis Krivine and Paul-Andr{\'e} Melli{\`e}s}, booktitle = {Interactive Models of Computation and Program Behavior}, series = {Panoramas et syntheses}, volume = {27}, publisher = {Soci{\'e}t{\'e} Math{\'e}matique de France}, pages = {15--215}, ) @inproceedings(scherer:simple:2015, author = {Gabriel Scherer and Ddier R{\'{e}}my}, year = {2015}, title = {Which Simple Types Have a Unique Inhabitant?}, booktitle = {Proceedings of the 20th {ACM} {SIGPLAN} International Conference on Functional Programming, ICFP~'15}, publisher = {{ACM}}, pages = {243--255}, doi = {10.1145/2784731.2784757}, ) @article(street:skew-closed:2013, author = {Ross Street}, year = {2013}, title = {Skew-Closed Categories}, journal = {Journal of Pure and Applied Algebra}, volume = {217}, number = {6}, pages = {973--988}, doi = {10.1016/j.jpaa.2012.09.020}, ) @article(szlachanyi:skew-monoidal:2012, author = {Korn{\'e}l Szlach\'anyi}, year = {2012}, title = {Skew-Monoidal Categories and Bialgebroids}, journal = {Advances in Mathematics}, volume = {231}, number = {3--4}, pages = {1694--1730}, doi = {10.1016/j.aim.2012.06.027}, ) @inproceedings(tomita:realizability:21, author = {Haruka Tomita}, year = {2021}, title = {Realizability without Symmetry}, editor = {Christel Baier and Goubault{-}Larrecq, Jean}, booktitle = {Proceedings of the 29th {EACSL} Annual Conference on Computer Science Logic, {CSL} 2021}, series = {Leibniz International Proceedings in Informatics}, volume = {183}, publisher = {Dagstuhl Publishing}, pages = {38:1--38:16}, doi = {10.4230/lipics.csl.2021.38}, ) @article(uustalu:eilenberg-kelly:2020, author = {Tarmo Uustalu and Niccol{\`o} Veltri and Noam Zeilberger}, year = {2020}, title = {{E}ilenberg-{K}elly Reloaded}, journal = {Electronic Notes in Theoretical Computer Science}, volume = {352}, pages = {233--256}, doi = {10.1016/j.entcs.2020.09.012}, ) @inproceedings(uustalu:deductive:nodate, author = {Tarmo Uustalu and Niccol{\'o} Veltri and Noam Zeilberger}, year = {2021}, title = {Deductive Systems and Coherence for Skew Prounital Closed Categories}, editor = {{Sacerdoti Coen}, Claudio and Alwen Tiu}, booktitle = {Proceedings of the 15th Workshop on Logical Frameworks and Meta-Languages: Theory and Practice, {LFMTP} 2020}, series = {Electronic Proceedings in Theoretical Computer Science}, volume = {332}, publisher = {Open Publishing Association}, pages = {35--53}, doi = {10.4204/eptcs.332.3}, ) @inproceedings(uustalu:proof:nodate, author = {Tarmo Uustalu and Niccol{\`o} Veltri and Noam Zeilberger}, year = {2021}, title = {Proof Theory of Partially Normal Skew Monoidal Categories}, editor = {David I. Spivak and Jamie Vicary}, booktitle = {Proceedings of the 3rd Annual International Applied Category Theory Conference 2020, {ACT} 2020}, series = {Electronic Proceedings in Theoretical Computer Science}, volume = {333}, publisher = {Open Publishing Association}, pages = {230--246}, doi = {10.4204/eptcs.333.16}, ) @incollection(uustalu:sequent:2021, author = {Tarmo Uustalu and Niccol{\`o} Veltri and Noam Zeilberger}, year = {2021}, title = {The Sequent Calculus of Skew Monoidal Categories}, editor = {Claudio Casadio and Philip J. Scott}, booktitle = {Joachim Lambek: The Interplay of Mathematics, Logic, and Linguistics}, series = {Outstanding Contributions to Logic}, volume = {20}, publisher = {Springer}, pages = {377--406}, doi = {10.1007/978-3-030-66545-6_11}, ) @inproceedings(veltri:coherence:2021, author = {Niccol{\`o} Veltri}, year = {2021}, title = {Coherence via Focusing for Symmetric Skew Monoidal Categories}, editor = {Alexandra Silva and Renata Wassermann and {de Queiroz}, Ruy}, booktitle = {Proceedings of the 27th International Workshop on Logic, Language, Information, and Computation, WoLLIC 2021}, series = {Lecture Notes in Computer Science}, volume = {13028}, publisher = {Springer}, pages = {184--200}, doi = {10.1007/978-3-030-88853-4_12}, ) @article(zeilberger:semiassociative:19, author = {Noam Zeilberger}, year = {2019}, title = {A Sequent Calculus for a Semi-Associative Law}, journal = {Logical Methods in Computer Science}, volume = {15}, number = {1}, eid = {9}, doi = {10.23638/lmcs-15(1:9)2019}, )