This is a very preliminary announcement for the International Conference in Category Theory next year. It will be held in Genoa (Italy) from Sunday, 21 June 2020, to Saturday, 27 June 2020. Information about registration, talk submission, and programme will be available in due time. See you next summer in Genoa! Beppe Metere, Sandra Mantovani, Pino Rosolini [For admin and other information see: http://www.mta.ca/~cat-dist/ ]