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Created intercategory.
Another creature in what you called the “zoo of higher categorical structures”. Is there some Linnaean taxonomy to help us put ’intercategory’, ’equipment’, etc. in their proper places?
Unfortunately not. A somewhat more systematic name for “equipment” that I’ve used in one place is “fibrant double category”, or with even more potential for generalization “fibrant 1x1-category”, but in addition to being longer that doesn’t carry the same connotation. The most systematic name I can think of for “intercategory” would be something like “laxly interchanging pseudo triple category”, and you can see why they wanted a snappier name for something important.
I see. Not too catchy.
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