Title: The Three Flavours of Morphisms Between Bicategories
Abstract: In everybody’s first course in category theory, we learn that categories have two different flavours of morphism: 0-morphisms (which are categories themselves), 1-morphisms (which are functors), and 2-morphisms (which are natural transformations). In this talk I’ll continue with our theme of “Geoff teaches everyone the magic of bicategories” by showing that this pattern of having multiple flavours of arrows continues with bicategories by introducing us to the 0-morphisms (which are bicategories), the 1-morphisms (which are pseudofunctors), the 2-morphisms (which are pseudonatural transformations), and the 3-morphisms (which are called modifications). Depending on time, we’ll also see various examples of these gadgets and how they can arise “in nature.”
