Let
be paths in
. Then
is thinly equivalent to
, denoted
, if there is a thin relative homotopy
between
and
.
We note that
is an equivalence relation, see
[2]. We use
to denote the
class of a path
and call
the semitrack of
. The groupoid
structure of
is induced by concatenation, +, of paths. Here one makes use of the fact that if
are paths then
there are canonical thin relative homotopies
The source and target maps
of
are given by
if
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