Weighted limits

[Jean Benabou <jean.benabou@wanadoo.fr>]

Dear all,

In section B1.1 of  the Elephant, weighted limits in a 2-category are
defined up to equivalence by pseudo cones. Let me say that strict
weighted limits exist if we can replace pseudo cones by genuine cones.
These limits are then defined up to a unique isomorphism.
In the category CAT of  categories (fill in universes if you don't
want to run into meta categories)  such strict limits exist.
Let me say that a 2-category is strictly finitely 2-complete if such
strict weighted limits exist for all finite (in an obvious sense)
weighted categories.

QUESTION:  Let S be a category with finite limits. I denote by Cat(S)
the 2-category of internal categories of S. Under which conditions on
S is Cat(S) strictly finitely 2-complete?

Best to all,

Jean


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