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Mar 10, 2017 at 11:47 comment added HeinrichD The construction only works if we assume that the monoidal category is locally presentable. If it is locally $\lambda$-presentable, and the tensor product preserves $\lambda$-directed colimits, then the transfinite construction needs $\lambda$ steps. Please let me know if you need more details. It might also be a good idea to contact Steve directly.
Feb 24, 2017 at 9:21 history asked Simon Henry CC BY-SA 3.0