Regular 2-categories

Richard Garner – 21 March 2012, 28 March 2012, 4 April 2012

This series of talks will give a thorough going-through of notions of regularity for 2-categories, making use of the theory of lex colimits developed with Steve Lack. Three notions of regularity will be considered, which respectively generalise to any suitable 2-category the (so, ioff), (bo, ff) and (bofull, faithful) factorisation systems on Cat. The main technical trick is to figure out the necessary exactness conditions by the requirement that there should exist a full structure preserving embedding into a sheaf 2-category (lex-reflective subcategory of a presheaf 2-category).

This is joint work with John Bourke.