Abstract:
We introduce a bipolar classification with index $j$ for endomorphisms of an arbitrary $n$-groupoid with $n>1$, where $j=1,2,\ldots,n$. The classifications of endomorphisms constructed generalize the bipolar classification of endomorphisms of an arbitrary groupoid (i.e., a $2$-groupoid) introduced previously. Using a left bipolar classification of endomorphisms of an $n$-groupoid (a particular case of the obtained classifications), we succeed in constructing an integral classification of endomorphisms of an arbitrary algebra (i.e., a structure without relations) with finitary operations.
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