Let $\mathscr{A}$ be a category and let $\parpairi{X}{Y}{s}{t}$ be objects and maps in $\mathscr{A}$. An equalizer of $s$ and $t$ is an object $E$ together with a map $E \stackrel{i}{\longrightarrow} X$ such that \(\xymatrix{ E \ar[r]^i & X \ar@<.5ex>[r]^s \ar@<-.5ex>[r]_t & Y }\) is a fork, and with the property that for any fork~, there exists a unique map $\bar{f}{\colon}\linebreak[0] A \to E$ such that \(\begin{array}{c} \xymatrix{ A \ar@{.>}[d]_{\bar{f}} \ar[rd]^f & \\ E \ar[r]_i &X } \end{array}\) commutes.