Factorizations of surjective maps of connected quandles

Abstract

We consider the problem of when one quandle homomorphism will factor through another, restricting our attention to the case where all quandles involved are connected. We provide a complete solution to the problem for surjective quandle homomorphisms using the structure theorem for connected quandles of Ehrman et al. (J. Knot Theory Ramifications 17:4 (2008), 511–520) and the factorization system for surjective quandle homomorphisms of Bunch et al. (J. Knot Theory Ramifications 19:9 (2010), 1145–1156) as our primary tools.