We give two proofs that the Euler characteristic is multiplicative, for fiber sequences of finitely dominated spaces. This is equivalent to proving that the Becker-Gottlieb transfer is functorial on π 0 \pi _0 .

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We give a short proof that the Yoneda embedding is natural for ∞ \infty -categories, and further prove that the space of natural transformations that are, pointwise, the Yoneda embedding, is contractible.