Dialgebra
In abstract algebra, a dialgebra is the generalization of both algebra and coalgebra. The notion was originally introduced by Lambek as "subequalizers",[1][2] and named as dialgebras by Tatsuya Hagino.[3][2] Many algebraic notions have previously been generalized to dialgebras.[4] Dialgebra also attempts to obtain Lie algebras from associated algebras.[5]
See also
[edit]References
[edit]- ^ Lambek, Joachim (1970). "Subequalizers". Canadian Mathematical Bulletin. 13: 337–349. doi:10.4153/CMB-1970-065-6. MR 0274552.
- ^ a b 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.
- ^ 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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