We all know about smoothing a crossing in a knot diagram: you replace the diagram with a sum of two diagrams that don't have crossings. But why does this make any sense? It turns out that the Jones polynomial is just one example of a functor between monoidal categories. We might also say that the Kauffman bracket is an example of a state function. I'll put some familiar things in a broader context by constructing a tangle invariant (or two!) different from our best-known example. When we smooth a crossing we'll get a sum of three diagrams, and one will have edges of two different colors meeting at trivalent vertices. We'll talk about what it all means.