What is the source of this famous Grothendieck quote? I've seen the following quote many times on the internet, and have used it myself. It is usually attributed to Grothendieck.

It is better to have a good category with bad objects than a bad category with good objects.

Question: Does anyone know the source of this quote, or at least when it first appears, or when it was first attributed to Grothendieck?
I wish I were able to properly cite this popular and insightful quote.

Added: On a related topic, another quote I wish I could cite properly, usually attributed to Manin, reads:

Proofs are more important than theorems, definitions are more important than proofs.

Does anyone know a source for this quote?
 A: Serre writes 

... comme Grothendieck nous l’a appris, les objets d’une catégorie ne jouent pas un grand rôle, ce sont les morphismes qui sont essentiels.

See page 335 in: J-P. Serre, Motifs, Journ. arithm. Luminy 1989 (Ed. G. Lachaud). Asterisque 198-200, Soc. Math. France, 1991, pp. 333-349. Although this quote is from 1991, of course it refers to the 50s and 60s.
Grothendieck's "relative way" of doing mathematics was apparent in most of his work. The first famous example is his generalization of Riemann-Roch.
A: Another quote in the spirit of that given by Martin Brandenburg.
In "Quelques idées maitresses de l'oeuvre de Grothendieck", Deligne writes

On reconnait la patte du Maitre dans l'idee que le probleme n'est pas de definir ce qu'est un motif: le probleme est de definir la categorie des motifs, et de degager les structures
  qu’elle porte.

which can be translated into

We recognize the touch of the Master in the idea that the problem is not to define what a motive is: the problem is to define the category of motives and to identify its structures.

A: In response to your second question, this is not precisely what you're looking for, but here is one quote by Yuri Manin along the same lines: 
All the other vehicles of mathematical rigor are secondary [to definitions], even that of rigorous proof. 
Manin makes this remark in an essay, entitled "Interrelations between Mathematics and Physics" that contains more memorable phrases, such as the final line of this extended quote:

All the other vehicles of mathematical rigor are secondary [to definitions], even that of rigorous proof. In fact, barring direct mistakes, the
  most crucial difficulty with checking
  a proof lies usually in the
  insufficiency of definitions (or lack
  thereof). In plain words, we are more
  deeply troubled when we wonder what
  the author wants to say than when we
  do not quite see whether what he or
  she is saying is correct. The flaws in
  the argument in a strictly defined
  environment are quite detectable. Good
  mathematics might well be written down
  at a stage when proofs are incomplete
  or missing, but informed guesses can
  already form a fascinating system:
  outstanding instances are A. Weil’s
  conjectures and Langlands’s program,
  but there are many examples on a
  lesser scale.
To the contrary, an inexperienced
  reader of the most interesting
  physical papers is often left in a
  vacuum about the precise meaning of
  the most common terms. Physicists are
  undoubtedly constrained by their own
  rules, but these rules are not ours.
  What is a current algebra, a
  supersymmetry transformation, a
  topological field theory, a path
  integral, finally? They are very open
  concepts, and it is precisely their
  openness that makes them so
  interesting. Here is what the history
  of our two metiers teaches: we cannot
  live without each other. At least for
  some of us, life becomes dull if it
  goes on for too long without contacts
  with good physics.
  In this century romantics comes from
  physics. Mathematics supplies hygienic
  habits and headaches.

A: I would be surprised if the purported Grothendieck quote is really his.  He does not lean to the short and sweet. It sounds more like an adaptation of another thing Deligne says in "Quelques idées maitresses de l'oeuvre de Grothendieck" (p. 13): "if the decision to let every commutative ring define a scheme gives standing to bizarre schemes, allowing it gives a category of schemes with nice properties."
