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Timeline for Pushforward and pullback.

Current License: CC BY-SA 2.5

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Nov 12, 2010 at 14:15 comment added Sándor Kovács I am not sure which part is giving you difficulties: "move" or "back and forth". One important point is that sheaves on $X$ and sheaves on $Y$ live in different categories, so in order to have them interact you have to "move" ("transport", "map" if you will) one of them to the other category. The "back and forth" is just a manner of speech: trying to indicate whether it goes from $X$ to $Y$ or vice versa. The arrow that stands for the map indicates a "direction" so you might as well say "forward" or "back".
Nov 11, 2010 at 16:43 comment added ε-δ Thank you. I do not have clear picture what is exactly "move them back and forth" (I only have bunch of examples). That makes me to feel bit uncomfortable. But it is better if everyone feels the same :)
Nov 11, 2010 at 7:26 history answered Sándor Kovács CC BY-SA 2.5