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Added an "Examples"-section to well-pointed topos and to Boolean topos mentioning Set and models for ETCS.
started a section well-pointed (oo,1)-topos as parts of the blog discussion here
In the course of that I added to the plain definition the statement that the global section functor is faithful
The pretopos section ends in a sentence I don’t know how to interpret:
But of course it applies whenever one is studying a pretopos.
Does this really mean topos here at the end? If not, what is “it”?
I think the “it” means this bit:
we have to strengthen the condition that 1 is a generator to the condition that 1 is a strong generator,
And I think the “whenever” means that it’s not just in thinking about a predicative category of sets, but an arbitrary pretopos.
added a separate definition of well-pointedness in terms of the axiom schemata of bounded separation (in addition to the terminal object being a strong generator), as defined in
Anonymous
added example of a coherent category satisfying the axiom of finiteness
Anonymous
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