Speaker: Julie Rasumsen – University of Warwick
Abstract: In recent years, several different attempts at developing the theory of enriched $\infty$-categories have been carried out by Gepner-Haugseng, Heine, and Hinich. These different approaches all have their advantages and disadvantages but have been shown to be equivalent. However, the theory is yet to be uniformly formulated using a single language, making it difficult to approach. In this talk, I will give a general overview of these different approaches and explain why intuitively, in particular, the approach by Gepner-Haugseng gives the desired structure. One key example is spectrally-enriched $\infty$-categories and how stable $\infty$-categories can be functorially considered as such. We will furthermore extend our understanding of enriched $\infty$-categories to enriched modules and their connection to enriched functors.