Clarify the definition of resolutions

Thanks to m.o.
http://stacks.math.columbia.edu/tag/09KQ#comment-536
Fix typos in categories.tex

Thanks to Nuno Cardoso
http://stacks.math.columbia.edu/tag/05PT#comment-538
Typo in homology.tex

Thanks to Nuno Cardoso
http://stacks.math.columbia.edu/tag/09SH#comment-539
Clarify statement lemma

Thanks to Nuno Cardoso
http://stacks.math.columbia.edu/tag/0A2E#comment-540
Used the wrong lemma

Thanks to Nuno Cardoso
http://stacks.math.columbia.edu/tag/0A2G#comment-542
Fix typos in derived.tex

Thanks to Nuno Cardoso
http://stacks.math.columbia.edu/tag/05SD#comment-543
Experimental change for display on website

Thanks to Niels Borne
http://stacks.math.columbia.edu/tag/00XI#comment-544
Fix typo in algebra.tex

Thanks to Paxton
http://stacks.math.columbia.edu/tag/05CD#comment-545