The ADJ group was a group of researchers founded in 1971 at the IBM T.J. Watson Research Center. It consisted of Joe Goguen (1941 - 2006), Jim Thatcher (1936 - 2019), Eric G. Wagner (1931 - 2021), and Jesse Wright. The purpose of the group was to promote the use of category theory and categorical algebra as a foundation for theoretical computer science.
One of the key contributions of the group was to connect the notion of initial algebra to McCarthy's notion of abstract syntax. See e.g. the classic paper [Goguen et al. 1977].
The ADJ name was supposed to be a moniker in the style of Bourbaki, and to also allude to adjunctions. [Goguen 1993] explains:
I proposed not only a working group, but also the rather grandiose project of providing a uniform, rigorous, abstract treatment of theoretical computer science, similar to what Bourbaki1 had done for mathematics, but using category theory explicitly, instead of secretly and implicitly, as Bourbaki had done. Surprisingly, this was agreed upon, and Jim Thatcher proposed the name ADJ as a (terrible) pun on the title of the book that we planned to write, "A Junction between Computer Science and Category Theory" (substitute "D" for the space between the initial "A" and the following "J" and recall that adjointness is a very important concept in category theory). We also agreed to use ADJ as a name for the set { Goguen, Thatcher, Wagner, Wright }, and to publish all our joint work under that name.
Goguen, Joseph A. 1993. ‘Memories of ADJ’. In Current Trends in Theoretical Computer Science, by G Rozenberg and A Salomaa, 76–81. World Scientific. https://doi.org/10.1142/9789812794499_0004. [ps]
@incollection{goguen_1993,
title = {Memories of {ADJ}},
urldate = {2023-05-14},
booktitle = {Current {Trends} in {Theoretical} {Computer} {Science}},
publisher = {World Scientific},
author = {Goguen, Joseph A.},
collaborator = {Rozenberg, G and Salomaa, A},
year = {1993},
doi = {10.1142/9789812794499_0004},
pages = {76--81}
}
Wagner, Eric G. 2002. ‘Algebraic Specifications: Some Old History and New Thoughts’. Nordic Journal of Computing 9 (4): 373–404. [ps]
@article{wagner_2002,
title = {Algebraic {Specifications}: some old history and new thoughts},
volume = {9},
url = {http://www.ii.uib.no/~wagner/MNotes/adjrun.ps},
number = {4},
journal = {Nordic Journal of Computing},
author = {Wagner, Eric G.},
year = {2002},
pages = {373--404}
}
Goguen, J. A., J. W. Thatcher, E. G. Wagner, and J. B. Wright. 1977. ‘Initial Algebra Semantics and Continuous Algebras’. Journal of the ACM 24 (1): 68–95.
@article{goguen_1977,
title = {Initial {Algebra} {Semantics} and {Continuous} {Algebras}},
volume = {24},
number = {1},
journal = {Journal of the ACM},
author = {Goguen, J. A. and Thatcher, J. W. and Wagner, E. G. and Wright, J. B.},
year = {1977},
pages = {68--95}
}