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I reclaimed this page as a disambiguation for horizontal/vertical and tight/loose terminology. Before that was just a redundant explanation of what a double category is, actually clashing with the main entry.
I thought Ehresmann introduced the horizontal/vertical terminology, but he didn’t. It’d be nice to track down who did to complete the picture.
I’m not sure the disambiguation is necessary: instead we can simply observe on the page that the terms “tight” and “loose” for F-categories are special cases of those for double categories (viewing an F-category as a strict double category with strict companions).
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