Theory around the Cellular Sheaf












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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.






reference-request algebraic-topology sheaf-theory sheaf-cohomology







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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






  • 1




    $begingroup$
    Sure, but I can't find an email address in your profile.
    $endgroup$
    – Vidit Nanda
    Apr 10 '16 at 16:58
















5












$begingroup$


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.






reference-request algebraic-topology sheaf-theory sheaf-cohomology







share|cite|improve this question









$endgroup$












  • $begingroup$
    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






  • 1




    $begingroup$
    Sure, but I can't find an email address in your profile.
    $endgroup$
    – Vidit Nanda
    Apr 10 '16 at 16:58














5












5








5


1



$begingroup$


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.






reference-request algebraic-topology sheaf-theory sheaf-cohomology







share|cite|improve this question









$endgroup$




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.






reference-request algebraic-topology sheaf-theory sheaf-cohomology




reference-request algebraic-topology sheaf-theory sheaf-cohomology






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked May 10 '15 at 18:48









ArrowArrow

5,21631546




5,21631546












  • $begingroup$
    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






  • 1




    $begingroup$
    Sure, but I can't find an email address in your profile.
    $endgroup$
    – Vidit Nanda
    Apr 10 '16 at 16:58


















  • $begingroup$
    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






  • 1




    $begingroup$
    Sure, but I can't find an email address in your profile.
    $endgroup$
    – Vidit Nanda
    Apr 10 '16 at 16:58
















$begingroup$
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




$begingroup$
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




$begingroup$
@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




1




1




$begingroup$
Sure, but I can't find an email address in your profile.
$endgroup$
– Vidit Nanda
Apr 10 '16 at 16:58




$begingroup$
Sure, but I can't find an email address in your profile.
$endgroup$
– Vidit Nanda
Apr 10 '16 at 16:58










2 Answers
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$begingroup$

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.






share|cite|improve this answer











$endgroup$





















    1












    $begingroup$

    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:




    • https://arxiv.org/abs/1808.01513






    share|cite|improve this answer









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      2 Answers
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      2 Answers
      2






      active

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      1












      $begingroup$

      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.






      share|cite|improve this answer











      $endgroup$


















        1












        $begingroup$

        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.






        share|cite|improve this answer











        $endgroup$
















          1












          1








          1





          $begingroup$

          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.






          share|cite|improve this answer











          $endgroup$



          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.







          share|cite|improve this answer














          share|cite|improve this answer



          share|cite|improve this answer








          edited Apr 6 '17 at 8:52

























          answered Apr 6 '17 at 1:11









          ಠ_ಠಠ_ಠ

          5,56621243




          5,56621243























              1












              $begingroup$

              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:




              • https://arxiv.org/abs/1808.01513






              share|cite|improve this answer









              $endgroup$


















                1












                $begingroup$

                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:




                • https://arxiv.org/abs/1808.01513






                share|cite|improve this answer









                $endgroup$
















                  1












                  1








                  1





                  $begingroup$

                  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:




                  • https://arxiv.org/abs/1808.01513






                  share|cite|improve this answer









                  $endgroup$



                  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:




                  • https://arxiv.org/abs/1808.01513







                  share|cite|improve this answer












                  share|cite|improve this answer



                  share|cite|improve this answer










                  answered Dec 19 '18 at 6:55









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