Differential of a Morphism

This lecture covers the concept of the differential of a morphism, which is a generalization of the differential known from analysis. It explains how to linearly approximate a map by using tangent spaces, defining the differential as a linear map between tangent spaces. The lecture also explores the properties of differentials, such as their behavior under composition and with constant maps. Additionally, it demonstrates the use of dual numbers to calculate differentials and provides examples of calculating differentials for matrix multiplication, emphasizing the importance of differentials in algebraic treatments.