Timeline for Fibrations using adjoints

9 events

when toggle format	what		by	license	comment
Jul 2 at 12:27	comment	added	Siya		Yes, well now I see from the first comment that all the liftings are up to iso. Hence we would have $Fh \cong h'$. Thanks, I will look at the conditions in which $F$ would actually be an isofibration.
Jul 1 at 23:09	comment	added	Mike Shulman		Sorry, I don't understand your question. Are you trying to prove that the map $g^*x \to x$ is cartesian?
Jun 30 at 22:56	comment	added	Siya		One last question, is there a reason why for any morphism $h \colon x \to g^* x$ in $C$, $Fh=h’$? For a morphism $h’ \colon x’ \to a$ in $D$. Or we have isomorphism instead of equality also.
Jun 27 at 21:12	comment	added	Mike Shulman		Yes, $g^*x \to U(a)$, I fixed it, thanks. And yes, as I said, if $F$ is not an isofibration, then you can only show that it's a Street fibration.
Jun 27 at 21:11	history	edited	Mike Shulman	CC BY-SA 4.0	added 3 characters in body
Jun 26 at 17:20	vote	accept	Siya
Jun 26 at 17:19	comment	added	Siya		Did you mean $F$ also maps the map $g^{*}a \to U(a)$ to an isomorphism? So the liftings are not up to equality but isomorphism, so $F$ would be a street fibration?
Jun 26 at 14:08	vote	accept	Siya
Jun 26 at 14:09
Jun 2 at 7:48	history	answered	Mike Shulman	CC BY-SA 4.0