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Definition 35.4.2. A split equalizer is a diagram (35.4.1.1) with $g_1 \circ f = g_2 \circ f$ for which there exist auxiliary morphisms $h : B \to A$ and $i : C \to B$ such that

35.4.2.1
\begin{equation} \label{descent-equation-split-equalizer-conditions} h \circ f = 1_ A, \quad f \circ h = i \circ g_1, \quad i \circ g_2 = 1_ B. \end{equation}

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View Definition 35.4.2 as pdf