Re: terminology of (co)algebras

[Michael Barr <barr@math.mcgill.ca>]

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


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