Timeline for What do you call the coherence cells in a lax morphism?

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Feb 25, 2016 at 18:00	comment	added	Mike Shulman		As a general term, I usually use "constraint" rather than "coherence", especially in the lax case. But either way, one can add add noun adjuncts to indicate the particular constraint: unit constraint, tensor product constraint, associativity constraint, etc.
Feb 25, 2016 at 13:34	comment	added	Dimitri Chikhladze		I usually refer to these things as "comparison" cells, maps, structure etc. It seemed to me a fairly common terminology.
Feb 25, 2016 at 5:07	comment	added	Qiaochu Yuan		Anyway, I think you want to give these cells names because there are situations where you want to point out that interesting information is hiding in them. For example, if you stare at the proof of Tannaka duality for finite groups, you crucially make use of the monoidor of the fiber functor in order to recover the group; without the monoidor, as explained at mathoverflow.net/questions/155743/…, you only recover the character table.
Feb 25, 2016 at 5:02	comment	added	Qiaochu Yuan		@Theo: I think you mean the "lax monoidor" and the "lax pointor," of course!
Feb 25, 2016 at 3:46	comment	added	Theo Johnson-Freyd		In the case of lax-monoidal functor $F$, I would call the natural transformation $F(X) \otimes F(Y) \to F(X\otimes Y)$ the "lax-monoidality data", and the morphism $1 \to F(1)$ the "lax pointing".
Feb 25, 2016 at 3:30	history	asked	Tim Campion	CC BY-SA 3.0