Semi-strictness in three-dimensional category theory and a (non-monoidal) closed structure on the category of Gray-categories (Part 2)

Adrian Miranda – 3 August 2022

Last week we looked at (semi) strictification in dimensions two and three, and we motivated the notion of a semi-strict trinatural transformation. This week we'll see a 'semi-strictification tetra-adjunction', and we'll see that semi-strict(ly decomposable) trinatural transformations feature in a closed structure on Gray-Cat. I'll also compare the closed structure to a monoidal structure on Gray-Cat due to Crans, and time permitting I'll talk about enrichment.