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I renamed familial regularity and exactness to k-ary exact category (with redirects from k-ary regular category), and updated some of the statements to match my exact completions paper a bit better.
I’m planning to create k-ary site as well, and add a statement of the main theorem of the paper somewhere on the nLab. But I’m undecided as to where that statement should go and how it should interact with the existing pages regular and exact completions and pretopos completion. Opinions are welcome.
I renamed familial regularity and exactness to k-ary exact category
Much better!
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