References

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