@book(adamekrosicky, author = {J.~Ad\'{a}mek and J.~Rosick\'{y}}, year = {1994}, title = {Locally Presentable and Accessible Categories}, series = {London Mathematical Society Lecture Note Series}, volume = {189}, publisher = {Cambridge University Press}, address = {Cambridge}, doi = {10.1017/CBO9780511600579}, ) @misc(nCafe, author = {J.~C. Baez}, year = {2019}, title = {Can 1+1 have more than two points?}, howpublished = {The $n$-Category Caf\'e}, url = {https://golem.ph.utexas.edu/category/2019/04/can_11_have_more_than_two_poin.html}, ) @incollection(baezstay, author = {J.~C. Baez and M.~Stay}, year = {2011}, title = {Physics, topology, logic and computation: a Rosetta Stone}, editor = {B.~Coecke}, booktitle = {New Structures for Physics}, publisher = {Springer}, address = {Berlin}, pages = {95--172}, doi = {10.1007/978-3-642-12821-9}, url = {https://arxiv.org/abs/0903.0340}, ) @book(barrwells, author = {M.~Barr and C.~Wells}, year = {1984}, title = {Toposes, Triples and Theories}, series = {Grundlehren der mathematischen Wissenschaften}, volume = {278}, publisher = {Springer}, address = {Berlin}, doi = {10.4204/EPTCS}, url = {https://www.math.mcgill.ca/barr/papers/ttt.pdf}, ) @article(beardsleywong, author = {J.~Beardsley and L.~Z. Wong}, year = {2019}, title = {The enriched Grothendieck construction}, journal = {Advances in Mathematics}, volume = {344}, pages = {234 -- 261}, doi = {10.1016/j.aim.2018.12.009}, url = {https://arxiv.org/abs/1804.03829}, ) @article(bkp, author = {R.~Blackwell and G.~M. Kelly and A.~J. Power}, year = {1989}, title = {Two-dimensional monad theory}, journal = {Journal of Pure and Applied Algebra}, volume = {59}, number = {1}, pages = {1--41}, doi = {10.1016/0022-4049(89)90160-6}, ) @book(borceux, author = {F.~Borceux}, year = {1994}, title = {Handbook of Categorical Algebra}, publisher = {Cambridge University Press}, address = {Cambridge}, doi = {10.1112/BLMS/28.4.440}, ) @book(crole, author = {R.~Crole}, year = {1994}, title = {Categories for Types}, publisher = {Cambridge University Press}, address = {Cambridge}, doi = {10.1017/CBO9781139172707}, ) @article(pseudo, author = {B.~Day and R.~Street}, year = {1997}, title = {Monoidal bicategories and Hopf algebroids}, journal = {Advances in Mathematics}, volume = {129}, number = {1}, pages = {99--157}, doi = {10.1006/aima.1997.1649}, ) @book(dubuc, author = {E.~J. Dubuc}, year = {1970}, title = {Kan Extensions in Enriched Category Theory}, series = {Lecture Notes in Mathematics}, volume = {145}, publisher = {Springer}, address = {Berlin}, doi = {10.1007/bfb0060485}, ) @inproceedings(fiore, author = {M.~Fiore and G.~Plotkin and D.~Turi}, year = {1999}, title = {Abstract syntax and variable binding}, booktitle = {Proceedings, 14th Symposium on Logic in Computer Science}, pages = {193--202}, ) @article(sset, author = {G.~Friedman}, year = {2012}, title = {An elementary illustrated introduction to simplicial sets}, journal = {Rocky Mountain Journal of Mathematics}, volume = {42}, number = {2}, pages = {353--423}, doi = {10.1216/rmj-2012-42-2-353}, ) @article(compeffects, author = {M.~Hyland and J.~Power}, year = {2006}, title = {Discrete Lawvere theories and computational effects}, journal = {Theoretical Computer Science}, volume = {366}, number = {1-2}, pages = {144--162}, doi = {10.1016/j.tcs.2006.07.007}, url = {https://core.ac.uk/download/pdf/81105779.pdf}, ) @article(hylandpower, author = {M.~Hyland and J.~Power}, year = {2007}, title = {The category theoretic understanding of universal algebra: Lawvere theories and monads}, journal = {Electronic Notes in Theoretical Computer Science}, volume = {172}, pages = {437--458}, doi = {10.1016/j.entcs.2007.02.019}, ) @book(jacobs, author = {B.~Jacobs}, year = {1998}, title = {Categorical Logic and Type Theory}, publisher = {Elsevier}, address = {Amsterdam}, doi = {10.1016/s0049-237x(98)x8028-6}, ) @book(joyal, author = {A.~Joyal}, year = {2008}, title = {The theory of quasicategories and its applications}, url = {http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.154.4968}, ) @article(kp, author = {P.\ Karazeris and G.\ Protsonis}, year = {2012}, title = {Left Kan extensions preserving finite products}, journal = {Journal of Pure and Applied Algebra}, volume = {216}, number = {8-9}, pages = {2014--2028}, doi = {10.1016/j.jpaa.2012.02.038}, ) @article(kelly, author = {G.~Kelly}, year = {2005}, title = {The Basic Concepts of Enriched Category Theory}, journal = {Reprints in Theory and Applications of Categories}, volume = {10}, doi = {10.1112/blms/15.1.96}, url = {http://www.tac.mta.ca/tac/reprints/articles/10/tr10abs.html}, ) @article(powsketch, author = {Y.~Kinoshita and J.~Power and M.~Takeyama}, year = {1999}, title = {Sketches}, journal = {Journal of Pure and Applied Algebra}, volume = {143}, number = {1-3}, pages = {275--291}, doi = {10.1016/s0022-4049(98)00114-5}, ) @article(lawvere, author = {F.~W. Lawvere}, year = {1963}, title = {Functorial semantics of algebraic theories}, journal = {Proceedings of the National Academy of Sciences}, volume = {50}, number = {5}, pages = {869--872}, doi = {10.1073/pnas.50.5.869}, url = {http://tac.mta.ca/tac/reprints/articles/5/tr5abs.html}, ) @incollection(linton, author = {F.~E.~J. Linton}, year = {1966}, title = {Some aspects of equational categories}, booktitle = {Proceedings of the Conference on Categorical Algebra}, publisher = {Springer}, pages = {84--94}, doi = {10.1007/978-3-642-99902-4$\relax$\@@underline {\hbox{\tmspace+\thickmuskip{.2777em}\tmspace+\thickmuskip{.2777em}}}\mathsurround\z@ $\relax$3}, ) @article(lucyshyn-wright, author = {Lucyshyn-Wright, R.~B.~B.}, year = {2015}, title = {Enriched algebraic theories and monads for a system of arities}, journal = {Theory and Applications of Categories}, volume = {31}, number = {5}, url = {http://www.tac.mta.ca/tac/volumes/31/5/31-05abs.html}, ) @incollection(ghani, author = {C.~L\"{u}th and N.~Ghani}, year = {1997}, title = {Monads and modular term rewriting}, booktitle = {Category Theory and Computer Science}, publisher = {Springer}, pages = {69--86}, doi = {10.1007/bfb0026982}, url = {http://www.informatik.uni-bremen.de/~cxl/papers/ctcs97l.pdf}, ) @book(milewski, author = {B.\ Milewski}, year = {2017}, title = {Category Theory for Programmers}, url = {https://bartoszmilewskiski.com/2017/08/26/lawvere-theories/}, ) @article(np, author = {K.~Nishizawa and J.~Power}, year = {2009}, title = {Lawvere theories enriched over a general base}, journal = {Journal of Pure and Applied Algebra}, volume = {213}, number = {3}, pages = {377--386}, doi = {10.1016/j.jpaa.2008.07.009}, ) @article(sos, author = {G.~D. Plotkin}, year = {2004}, title = {A structural approach to operational semantics}, journal = {Journal of Logical and Algebraic Methods in Programming}, volume = {60-61}, pages = {17--139}, doi = {10.1016/j.jlap.2004.05.001}, url = {http://homepages.inf.ed.ac.uk/gdp/publications/sos_jlap.pdf}, ) @article(power, author = {J.~Power}, year = {1999}, title = {Enriched Lawvere theories}, journal = {Theory and Applications of Categories}, volume = {6}, number = {7}, pages = {83--93}, url = {http://www.tac.mta.ca/tac/volumes/6/n7/6-07abs.html}, ) @article(combs, author = {M.~Sch\"{o}nfinkel}, year = {1924}, title = {Bausteine zu einer Logik der mathematischen Wissenschaften}, journal = {Mathematische Annalen}, volume = {92}, pages = {305--316}, url = {http://www.digizeitschriften.de/dms/img/?PID=GDZPPN002270110}, ) @incollection(seely, author = {R.~A.~G. Seely}, year = {1987}, title = {Modelling computations: a 2-categorical framework}, booktitle = {Proceedings of the Second Annual IEEE Symposium on Logic in Computer Science}, publisher = {IEEE Computer Society Press}, address = {Ithaca, New York}, pages = {22--25}, ) @misc(roswelt, author = {M.~Stay and L.~G. Meredith}, year = {2017}, title = {Representing operational semantics with enriched Lawvere theories}, url = {https://arxiv.org/abs/1704.03080}, ) @misc(ladl, author = {M.~Stay and L.~G.~Gregory Meredith}, year = {2016}, title = {Logic as a distributive law}, url = {https://arxiv.org/abs/1610.02247}, )