Dialgebra Explained

In abstract algebra, a dialgebra is the generalization of both algebra and coalgebra. The notion was originally introduced by Lambek as "subequalizers",^[1] and named as dialgebras by Tatsuya Hagino.^{[2] [3]} Many algebraic notions have previously been generalized to dialgebras.^[4] Dialgebra also attempts to obtain Lie algebras from associated algebras.^[5]

See also

• F-algebra

Further reading

• dialgebra in nLab

Notes and References

1. Lambek . Joachim . 10.4153/CMB-1970-065-6 . Canadian Mathematical Bulletin . 274552 . 337–349 . Subequalizers . 13 . 1970.
2. Hagino . Tatsuya . Pitt . David H. . Poigné . Axel . Rydeheard . David E. . A typed lambda calculus with categorical type constructors . 10.1007/3-540-18508-9_24 . 140–157 . Springer . Lecture Notes in Computer Science . Category Theory and Computer Science, Edinburgh, UK, September 7–9, 1987, Proceedings . 283 . 1987.
3. Backhouse . Roland . Hoogendijk . Paul . 10.1051/ita:1999126 . 4-5 . RAIRO Theoretical Informatics and Applications . 1748664 . 401–426 . Final dialgebras: from categories to allegories . 33 . 1999.
4. Poll . Erik . Zwanenburg . Jan . Corradini . Andrea . Lenisa . Marina . Montanari . Ugo . From algebras and coalgebras to dialgebras . https://www.cs.ru.nl/E.Poll/papers/cmcs01.pdf . 10.1016/S1571-0661(04)80915-0 . 1 . 289–307 . Elsevier . Electronic Notes in Theoretical Computer Science . Coalgebraic Methods in Computer Science, CMCS 2001, a Satellite Event of ETAPS 2001, Genova, Italy, April 6–7, 2001 . 44 . 2001. 2066/19049 . free .
5. Book: Loday, Jean-Louis . Loday . Jean-Louis . Chapoton . Frédéric . Frabetti . Alessandra . Goichot . François . Dialgebras . 10.1007/3-540-45328-8_2 . 3-540-42194-7 . 1860994 . 7–66 . Springer . Lecture Notes in Mathematics . Dialgebras and Related Operads . 1763 . 2001 . 0999.17002.