nLab
split equalizer
A fork
A\xrightarrow[\quad e \quad]{}B\underoverset{\quad g \quad}{f}{\rightrightarrows}C
is split if it can be embedded into a diagram
A\xrightarrow[\quad e \quad]{\overset{\scriptsize{s}}{\begin{svg}
<svg width="31" height="11" xmlns="http://www.w3.org/2000/svg" xmlns:se="http://svg-edit.googlecode.com" se:nonce="56258">
<g>
<title>Layer 1</title>
<path fill="none" stroke="#000000" d="m2.436699,8.563251c9.440479,-9.454929 17.148819,-9.609211 27.625038,0.192581" marker-start="url(#se_marker_start_svg_56258_3)" id="svg_56258_3"/>
</g>
<defs>
<marker refY="50" refX="50" markerHeight="5" markerWidth="5" viewBox="0 0 100 100" orient="auto" markerUnits="strokeWidth" id="se_marker_start_svg_56258_3">
<path stroke-width="10" stroke="#000000" fill="#000000" d="m0,50l100,40l-30,-40l30,-40l-100,40z" id="svg_56258_7"/>
</marker>
</defs>
</svg>
\end{svg}\includegraphics[width=23]{curvedArrow1}
}}B\underoverset{\quad g \quad}{\mathclap{\overset{\scriptsize{t}}{\begin{svg}
<svg width="33" height="18" xmlns="http://www.w3.org/2000/svg" xmlns:se="http://svg-edit.googlecode.com" se:nonce="69468">
<g>
<title>Layer 1</title>
<path marker-start="url(#se_marker_start_svg_69468_2)" id="svg_69468_2" d="m2.12632,15.467968c13.519966,-19.398649 19.108238,-19.52702 30.125008,0.027042" stroke="#000000" fill="none"/>
</g>
<defs>
<marker refY="50" refX="50" markerHeight="5" markerWidth="5" viewBox="0 0 100 100" orient="auto" markerUnits="strokeWidth" id="se_marker_start_svg_69468_2">
<path stroke-width="10" stroke="#000000" fill="#000000" d="m0,50l100,40l-30,-40l30,-40l-100,40z" id="svg_69468_6"/>
</marker>
</defs>
</svg>
\end{svg}\includegraphics[width=24]{curvedArrow2}
}}f}{\rightrightarrows}Cin which , and (we used here Leibniz order for composition of morphisms).
Surely, and can be interchanged in the definition (a matter of unimportant convention).
Every split fork is an absolute equalizer, but not conversely. See also split coequalizer.