Timeline for A (too easy) normalization of a lax-funtor between 2-categories ?
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| Nov 1, 2012 at 17:37 | comment | added | Buschi Sergio | THank you very much Jonatan (I'm no a researcher, I study alone after job, and sometime I'm tired and I take misunderstandings for stress or enthusiasm). Anyway for pseudonfunctors I seems that is possible correct the HOm-functors (functors inducted between Hom-categories) | |
| Nov 1, 2012 at 11:50 | comment | added | Jonathan Chiche | Well, I know what the axioms are, but part of my point is that some of these axioms are missing in your question. For instance, you don't mention the fact that lax functors induce functors between the categories of 1-cells. I don't think this condition is automatically satisfied as soon as the ones you mention are, even in the realm of (strict) 2-categories. | |
| Nov 1, 2012 at 10:55 | comment | added | Buschi Sergio | Of course the axioms are the classical: J.Benabou, Introduction to bicategories, (M1) and (M2) p. 30. Thank your for the reference. A lax functors (for me) is what J.Benabou call morphisms (of bicategories) or what J.W. Gray call "pseudo.functors" in its "Formal category theory" LNM 391, 1974. A lax.functor $F$ (for me) is normal if the canonical cell $1_{F(X)}\Rightarrow F(1_X)$ is the identity. | |
| Nov 1, 2012 at 10:16 | history | answered | Jonathan Chiche | CC BY-SA 3.0 |