# Stacks are just sheaves up to Isomorphism

I have heard that one can think of stacks on a site as taking sheaves but instead of the restrictions being equal, we just loosen it to isomorphic, and treat the sheaf conditions with the "obvious" coherence relations.

How seriously can one take this analogy? Note that my background is stacks is feeble at best.

I hope this question isn't too vague. One may choose to respond to this question with "That analogy is stupid because of __ gotcha".

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Maybe you will find useful ncatlab.org/nlab/show/stack (and links there). – Grigory M Jul 25 '10 at 10:02
Yea, I have taken a look at that, in fact part of this intuition came from reading that, but I find it difficult to extract the answer to my question from that discussion because it is so rough. – BBischof Jul 25 '10 at 19:16
I think the title of this question is incorrect/misleading, and should be changed/fixed. Maybe to "Stacks are sheaves of groupoids"? – Kevin H. Lin Jul 29 '10 at 9:52