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Jan 18, 2010 at 16:57 comment added darij grinberg Oops. You are totally right, fixed.
Jan 18, 2010 at 16:56 history edited darij grinberg CC BY-SA 2.5
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Jan 18, 2010 at 16:01 comment added Mariano Suárez-Álvarez In you second generalization, you need either $U_i=V_i$ for all $i$, or the vector spaces need to have chosen bases, and the complexes should be exact (consider otherwise complexes with zero differential!)
Jan 18, 2010 at 15:46 history answered darij grinberg CC BY-SA 2.5