Clarification on 2-categories

Hi all,

Note: Fix a 2-category A throughout. Composition of 1-cells is denoted
by concatenation. The same for the horizontal composition of 2-cells.
I'll use greek LaTeX for 2-cells, e.g. \phi, \tau, etc.

I'm reading a short intro on 2-categories by J. Power. At some point
he speaks about a special kind of limits. Take the case of equifiers:
If you have two parallel 1-cells f,g:a->b then the equifier of f,g is
a 1-cell e:c->a equipped with a two cell \phi:fe->ge universal among
such pairs. That is, if (\phi',e') is another pair with
\phi':fe'->ge', then there is a unique 1-cell h such that

\phi h = \phi'

What is not clear to me is if there is a corresponding factorization
property for 2-cells in the equifier definition? I assume a 2-cell
between equifier pairs (\phi,e)->(\phi',e') would be a 2-cell \tau
such that \phi \tau = \phi'. Anyone?

The same question for inserters.

TIA, with my best regards,
G. Rodrigues
.