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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeOct 14th 2010

started stub for bounded geometric morphism

• CommentRowNumber2.
• CommentAuthorDavid_Corfield
• CommentTimeJan 9th 2016

I corrected the characterisation of boundedness.

• CommentRowNumber3.
• CommentAuthorTodd_Trimble
• CommentTimeJan 9th 2016

Why don’t you just say quotient of a subobject of …, instead of subquotient of a subobject of …?

• CommentRowNumber4.
• CommentAuthorDavid_Corfield
• CommentTimeJan 9th 2016
• (edited Jan 9th 2016)

Oh I see. It was fine as it was. I’ll roll back, but fix a typo.

• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeJun 10th 2016
• (edited Jun 10th 2016)

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!

• CommentRowNumber6.
• CommentAuthorJonasFrey
• CommentTimeJun 13th 2016

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.

• CommentRowNumber7.
• CommentAuthorUrs
• CommentTimeJun 13th 2016

Thanks!

• CommentRowNumber8.
• CommentAuthorjonsterling
• CommentTimeNov 17th 2021

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?

• CommentRowNumber9.
• CommentAuthorUrs
• CommentTimeNov 17th 2021
• (edited Nov 17th 2021)

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!