**Puzzle 279**
Here's my attempt:
![tensoring](https://raw.githubusercontent.com/ikshv/categories/master/tensors.png?sanitize=true)

To show that \$$h = f' \circ f\$$ and \$$e = g' \circ g\$$ (Exercise 278), we need the triangles in the picture (bottom) commute. Here I stuck - while \$$f' \circ f\$$ and \$$g' \circ g \$$ are natural candidates for \$$h\$$ and \$$e\$$ respectively, they are not the only ones.

One possible explanation is that we need the morphisms \$$f \otimes g \$$ and \$$f' \otimes g'\$$ of the \$$C \times C\$$ category to be composable, such that \$$(f' \otimes g') \circ (f \otimes g) = (h \otimes e)\$$, and this in turn implies that \$$h = f'\circ f\$$ and \$$e = g'\circ g\$$, but I'm waiting for a more formal explanation.