I am not sure if I was the first, but I defined T-algebras for an endofunctor T in my paper, Coequalizers and free triples. You can find it at http://www.math.mcgill.ca/barr/papers/#1970s, it being my first 1970s paper. As the name suggests, the category of T-algebras is often tripleable. Michael ----- Original Message ----- From: "Jiri Adamek" <adamek@iti.cs.tu-bs.de> To: "categories net" <categories@mta.ca> Sent: Friday, October 9, 2015 9:27:54 AM Subject: categories: terminology of (co)algebras Does anyone know who was the first author to speak about F-algebras and/or F-coalgebras where F is a mere endofunctor? Lambek proved his famous lemma without using any name for the objects. And Arbib and Manes proved a number of properties but used the word "F-dynamics". Thanks Jiri [For admin and other information see: http://www.mta.ca/~cat-dist/ ] [For admin and other information see: http://www.mta.ca/~cat-dist/ ]