20 Sep
2007
20 Sep
'07
11:23 p.m.
Josh Nichols-Barrer wrote:
Is there a name for a weak functor between bicategories which takes identity 1-morphisms to identity 1-morphisms?
The term 'normalised' (already mentioned in the replies) goes back at least to Grothendieck, SGA1, Exp VI: he calls a cleavage for a fibred category E -> B normalised if the cartesian lift of each identity arrow is an identity arrow -- this is exactly the condition for the correponding pseudo-functor B^op -> Cat to preserve identity arrows strictly. Joachim.