Abstract
There have been two distinct approaches to quasigroup homotopies, through reversible automata or through semisymmetrization. In the current paper, these two approaches are correlated. Kernel relations of homotopies are characterized combinatorically, and shown to form a modular lattice. Nets or webs are exhibited as purely algebraic constructs, point sets of objects in the category of quasigroup homotopies. A factorization theorem for morphisms in this category is obtained.
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