Exercise 1.3.9. Show that the fiber product is commutative, associative and unital: for functors \(C\to E\), \(D \to E\) and \(B \to E\), there are equivalences \[ C \times _{E} D \iso D \times _{E} C, \qquad B \times _{E} (C \times _{E} D) \iso (B \times _{E} C) \times _{E} D, \qquad C \times _{E} E \iso C. \]
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