The category meeting in Carvoeiro, Portugal held from June 17th to 23rd, 2007 proved to be one of the most enjoyable and scientifically promising of the series. This was possible because of the thoughtful and dedicated organization by Diana Rodelo, Manuela Sobral, Maria Manuel Clementino, Jorge Picado, Lourdes Sousa, Gonzalo Gutierres, and Maria Joao Ferreira. They created a wonderful atmosphere which made possible the collaboration and friendship between the senior researchers who were there and the many very intelligent and active young people, who will be contributing their original research to future meetings. Of course, I was particularly honored by the fact that the conference banquet took note of my 70th birthday and was attended by several of my cherished students and colleagues. I was gratified to meet the many young researchers whom I had not previously known; they gave me the special gift of hope for the future of our science. My friends and colleagues join me in heartily thanking the organizers, the scientific committee, and the sponsoring organizations for having created a most memorable occasion. Bill Lawvere ************************************************************ F. William Lawvere, Professor emeritus Mathematics Department, State University of New York 244 Mathematics Building, Buffalo, N.Y. 14260-2900 USA Tel. 716-645-6284 HOMEPAGE: http://www.acsu.buffalo.edu/~wlawvere ************************************************************