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

There are also:

• 4 comment(s) on Section 35.4: Descent for universally injective morphisms

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).