Lemma 4.31.9. Let
be a commutative diagram of categories and functors. Then there is a canonical functor
of categories.
Lemma 4.31.9. Let
be a commutative diagram of categories and functors. Then there is a canonical functor
of categories.
Proof. If we write \mathcal{A} \times _\mathcal {B} \mathcal{C} \times _\mathcal {D} \mathcal{E} as (\mathcal{A} \times _\mathcal {B} \mathcal{C}) \times _\mathcal {D} \mathcal{E} then we can just use the functor
if you know what I mean. \square
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