Binary products and coproducts of categories

Notation 1.3.3. When \(I = \{1,2\}\), we write \(C_1 \times C_2\) and \(C_1 \sqcup C_2\) for the resulting product and coproduct. Given functors \(f_1\colon T \to C_1\) and \(f_2\colon T \to C_2\), we write \((f_1,f_2)\colon T \to C_1 \times C_2\) for the induced functor. Given functors \(g_1\colon C_1 \to T\) and \(g_2\colon C_2 \to T\), we write \(\lra {g_1,g_2}\colon C_1 \sqcup C_2 \to T\) for the induced functor.