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Stream: learning: questions

Topic: reflective subcategory

Jan Pax (Aug 19 2022 at 15:08):

Does it make any difference, in the definition of a reflective subcategory, if the reflection induced by $f$ goes directly to the codomain of $f$ or if we, on the contrary, insert a reflection between codomain of $f$ and codomain of the reflection induced by $f$. In the former case it is understood that $f$ lies in the entire category while in the latter case that it targets to the reflective part. 111-kopie.jpg Obviously $(2)\Longrightarrow(1)$