Graded Monoidal Categories and Internalization
In this paper, which began as my University of Chicago REU (2022) project and later became my undergraduate thesis, I establish a general categorical framework for transforming “external” graded monoidal products into classical “internal” monoidal products. This makes an analogy between the constructions of Day convolution and the smash product of S-modules formal, as they are both manifestations of internalized graded monoidal products, allowing properties of these products to be recovered via abstract nonsense.