Adjoints in linear algebra and category theory

Adjoints in linear algebra and category theory

The previous post looked at adjoints in the context of linear algebra. This post will look at adjoints in the context of category theory. The adjoint of a linear operator T between inner product spaces V and W is the linear operator T* such that for all v in V and all w in W, ⟨ Tv, w ⟩W = ⟨ v, T*w ⟩V. The subscripts are important because the left side is an inner product in W and the right side is an inner product in V. Think of the inner produc…