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I have lately stumbled upon cellular (co)sheaves, which look very interesting. To understand them better, I would like references that systematically develop the theory behind them (preferably in categorical fashion), and/or provide geometric intuition for their workings.

So far, the best source of information I have found is Curry's Sheaves, Cosheaves, and Applications.

All recommendations are welcome. In particular, I am also looking for Shepard A.D's 1985 thesis A Cellular Description of the Derived Category of a Stratified Space, a copy of which I have not been to find anywhere.

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  • $\begingroup$ The two sources you mention (Curry and Sheppard) are literally the only references out there, and as far as I can see, both liberally use categorical terminology. What are you looking for that can't be found there? $\endgroup$ – Vidit Nanda Apr 10 '16 at 4:19
  • $\begingroup$ @ViditNanda I would like, for instance, to have a copy of Sheppard's thesis. Could you by any chance mail one to me? $\endgroup$ – Arrow Apr 10 '16 at 7:52
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    $\begingroup$ Sure, but I can't find an email address in your profile. $\endgroup$ – Vidit Nanda Apr 10 '16 at 16:58
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Robert Ghrist's Elementary Applied Topology defines and works with cellular sheaves in chapter 9. He doesn't introduce category theory until later, but he is good at giving geometric motivation and applications.

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there is also a book from Michael Robinson: "Topological Signal Processing". chapters 3, 4, 5 and 6 deal with cellular-sheaves. However, Robinson only adresses the question of categories in chapter 4, and doesn't use it at all to define the cellular sheaves (which in my view, makes it less clear). It is however full of examples which can reveal useful.

For a better structured but shorter introduction to cellular sheaves, I would recommend the first sections of the article "Toward a Spectral Theory of Cellular Sheaves" by Hansen and Ghrist available on arXiv:

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