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started stub for bounded geometric morphism
I corrected the characterisation of boundedness.
Why don’t you just say quotient of a subobject of …, instead of subquotient of a subobject of …?
Oh I see. It was fine as it was. I’ll roll back, but fix a typo.
Jonas Frey has kindly added some material to the Properties-section at bounded geometric morphism. I have touched the formatting a little and added some more cross-links with the entry internal sheaf.
Notice that the entry is still waiting for somebody to complete two items in its Definition section!
I filled in the holes in the definition by copying the missing parts from the elephant, and rephrasing a bit.
The equivalent reformulations use terminology that needs to be defined, therefore I amended separating family, adding the definition of separating family in a fibration.
The concept of gluing fibration still needs to be defined – probably by remarking on the page on Artin gluing that the appropriate projection is a fibration. I’ll come back to that maybe tomorrow.
Thanks!
I think that the statement about the gluing fibration should be $\partial_1$ not $\partial_0$ right? We are restricting the codomain fibration along the inverse image of the geometric morphism, not the domain functor. Right?
We are talking about this line, supposedly).
But $\partial_0$ is the codomain, in usual simplicial conventions (remove the 0-vertex!)
In any case, for the moment I have removed the symbol “$\partial_0$” (it’s not too illuminating and never appears again, anyway). Somebody should indicate the actual definition of that morphism!
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