Moufang Loops and Groups with Triality are Essentially the Same Thing

In 1925 Elie Cartan introduced the principal of triality specifically for the Lie groups of type $D_4$, and in 1935 Ruth Moufang initiated the study of Moufang loops. The observation of the title in 1978 was made by Stephen Doro, who was motivated by George Glauberman. Here the author makes the statement precise in a categorical context.