Michael Barr writes:
Back in the mid 60s, I read a paper (or maybe a preprint) by John Moore showing that simplicial groups are Kan complexes. As I look through MathSciNet, I can find nothing like that among Moore's publications. Does anyone know if this was published or does anyone have a copy? Or can anyone give me a reference for the fact?
Michael
To answer the last question first the fact is Lemma 3.4 (credited to Moore) in Paul G. Goerss, John F. Jardine Simplicial Homotopy Theory Birkhauser (1999) I believe Moore published it as part of his outline of simplicial theory in @incollection {MR0111027, AUTHOR = {Moore, John C.}, TITLE = {Semi-simplicial complexes and {P}ostnikov systems}, BOOKTITLE = {Symposium internacional de topolog\'\i a algebraica International symposium on algebraic topology}, PAGES = {232--247}, PUBLISHER = {Universidad Nacional Aut\'onoma de M\'exico and UNESCO, Mexico City}, YEAR = {1958}, MRCLASS = {55.00}, MRNUMBER = {MR0111027 (22 \#1894)}, MRREVIEWER = {J. A. Zilber}, } and that the notes you reference were from his 1956 Princeton Seminar on Algebraic Homotopy Theory. I have long since lost my copy of the notes, and cannot find a copy of the above paper, so these last two have to be considered speculative memories. -- Bob -- Robert L. Knighten Robert@Knighten.org