  The purpose of this letter is to point out a relation between the boundary
condition satisfied by spherically symmetric isolated horizons (formulated in
terms of Ashtekar-Barbero variables) and the source-target matching condition
(also known as fake flatness condition) in higher gauge theory. This relation
may prove useful in the attempt to quantize the isolated horizon boundary
condition which is in turn a possible starting point for the search for black
hole solutions in the full theory of loop quantum gravity. Also, since a
2-connection is the mathematical object required for describing the parallel
transport of 1-dimensional objects, the relation presented in this letter may
provide further insight into the coupling of LQG to string-like objects
investigated in other contexts.
