Abstract.  

A quasigroup (combinatorially a Latin Square) maybe thought of as a set with a multiplication such that both the right and left multiplication maps determined by any particular element of the quasigroup are bijections. The relation "is isotopic to" is an equivalence relation on the category of quasigroups. We will look at examples of quasigroups as well as a couple of results:

1] in every equivalence class of the relation "is isotopic to" there is a loop

2] if a group, H, is in an equivalence class of the relation "is isotopic to" then every element of the equivalence class is a group isomorphic to H.