What's the name of this flavor of n-category? I'm looking for the name of a certain n-category definition.  (Someone explained it to me a couple of years ago.  I remember the definition, but not the name.  Without the name it's difficult to search for a citation.  I want the citation in order to explain something we're not doing in a paper.)
For background, consider the Moore loop space $\Omega_r$ of loops of length $r$  (that is, parameterized by the interval $[0,r]$).  We have a strictly associative composition $\Omega_r\times \Omega_s\to \Omega_{r+s}$.  The main idea of an "xxxx" n-category is to imitate this idea in higher dimensions.  The $k$-morphisms are parameterised by $k$-dimensional rectangles with sides of lengths $r_1,\ldots,r_k$.  Gluing rectangles together gives $k$ different strictly associative ways to compose $k$-morphisms.
Question:  What is "xxxx" above?
Bonus question:  What's the best (or any) citation for this idea?

EDIT: It turns out the definition I was trying to remember is unpublished work of Ulrike Tillmann.  But the version from Ronnie Brown linked to in David Roberts' answer is pretty similar (for my purposes, at least).
 A: Ronnie Brown has a related idea, contained in this article:

Moore hyperrectangles on a space form a strict cubical omega-category
arXiv

discussed briefly here at the nLab.
If you are instead thinking of a globular $n$-category, the closest I know of is a Trimble n-category, but that doesn't use Moore paths, but paths of length 1 and the $A_\infty$-co-category structure on $[0,1]$.
A: Simpson-semistrict $n$-categories could be what you're after: $n$-categories where everything except the unit laws holds strictly, generalising one of the crucial properties of Moore path spaces?  It's not a specific definition of $n$-category, but a strictness property which can be applied within various definitions.
Carlos Simpson has conjectured that these are enough to model homotopy types; Moore path space show this in dimension 1.  I know very little about the details of this myself, I'm afraid, but what I have read about it is mostly from these sources plus their links and discussions:


*

*Simpson, Homotopy types of strict 3-groupoids.

*nlab: semi-strict $\infty$-category

*nlab: Simpson’s conjecture (I can't figure out how to link this directly; the single-quote in the url seems to confuse markdown)

*n-Category Café: Urs Schreiber, Semistrict Infinity-Categories and ω-Semi-Categories
I believe several people have been making some progress on it recently; eg Makkai mentioned some results along these lines at the latest Octoberfest.
