In abstract algebra, a dialgebra is the generalization of both algebra and coalgebra. The notion was originally introduced by Lambek as "subequalizers", and named as dialgebras by Tatsuya Hagino. Many algebraic notions have previously been generalized to dialgebras. Dialgebra also attempts to obtain Lie algebras from associated algebras.
See also
References
- Lambek, Joachim (1970). "Subequalizers". Canadian Mathematical Bulletin. 13 (3): 337–349. doi:10.4153/CMB-1970-065-6. MR 0274552.
- ^ Backhouse, Roland; Hoogendijk, Paul (1999). "Final dialgebras: from categories to allegories" (PDF). RAIRO Theoretical Informatics and Applications. 33 (4–5): 401–426. doi:10.1051/ita:1999126. MR 1748664.
- Hagino, Tatsuya (1987). "A typed lambda calculus with categorical type constructors". In Pitt, David H.; Poigné, Axel; Rydeheard, David E. (eds.). Category Theory and Computer Science, Edinburgh, UK, September 7–9, 1987, Proceedings. Lecture Notes in Computer Science. Vol. 283. Springer. pp. 140–157. doi:10.1007/3-540-18508-9_24. ISBN 978-3-540-18508-6.
- Poll, Erik; Zwanenburg, Jan (2001). "From algebras and coalgebras to dialgebras" (PDF). In Corradini, Andrea; Lenisa, Marina; Montanari, Ugo (eds.). Coalgebraic Methods in Computer Science, CMCS 2001, a Satellite Event of ETAPS 2001, Genova, Italy, April 6–7, 2001. Electronic Notes in Theoretical Computer Science. Vol. 44 (1 ed.). Elsevier. pp. 289–307. doi:10.1016/S1571-0661(04)80915-0. hdl:2066/19049.
- Loday, Jean-Louis (2001). "Dialgebras". In Loday, Jean-Louis; Chapoton, Frédéric; Frabetti, Alessandra; Goichot, François (eds.). Dialgebras and Related Operads. Lecture Notes in Mathematics. Vol. 1763. Springer. pp. 7–66. doi:10.1007/3-540-45328-8_2. ISBN 3-540-42194-7. MR 1860994. Zbl 0999.17002.
Further reading
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