@John A few typos in the lecture:

1. A couple of feasbility relations use the wrong type of arrow:
in the introduction, \$$\Phi \colon X \to Y \$$ should be \$$\Phi \colon X \nrightarrow Y\$$;
in puzzle 207, \$$\Psi \Phi : \mathbb{N} \to [0,\infty) \$$ should be \$$\Psi \Phi : \mathbb{N} \nrightarrow [0,\infty) \$$.

2. In the definition of tensoring \$$\Phi'\$$ should be \$$\Psi\$$.

3. In puzzle 207, I think the feasability relations compose the other way around, that is, it should have been \$$\Phi \Psi : \mathbb{N} \nrightarrow [0,\infty) \$$.