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• CommentRowNumber1.
• CommentAuthorTim Campion
• CommentTimeMar 18th 2016

It’s kind of strange to have separate pages for compactly generated (∞,1)-category and locally presentable (∞,1)-category, since they are really terminological variants of each other. There’s a grammatical difference in how Lurie uses them: for him, “[locally] presentable ∞-category” leaves the degree of accessibility unspecified, whereas “compactly-generated” sets the degree of accessibility at $\kappa = \omega$. When he wants to specify the degree of accessibility, he has a choice between “[locally] $\kappa$-presentable” and “$\kappa$-compactly-generated”; he opts for the latter. At the very least, these articles should be modified to better reflect this.

• CommentRowNumber2.
• CommentAuthorTim Campion
• CommentTimeMar 20th 2016

I’ve made some changes to those two pages as well as accessible (∞,1)-category to better reflect this. If anyone feels like merging the pages, that might be a reasonable thing to do.

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeMar 21st 2016
• (edited Mar 21st 2016)

Thanks for this, that’s a good point. The entries could have been organized a bit better, that’s true. Thanks for adding clarifications. Myself, I don’t have the energy to look into it right now, but feel invited to edit further if or when you feel like it.