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I’m going to start reading Kashiwara-Shapira’s trilogy Categories and Sheaves, Sheaves on Manifolds, and Perverse Sheaves with someone soon. Flipping through the table of contents for Sheaves on Manifolds (SM), it seems like we could read either Cats n Sheaves or SM first. Which would you recommend we start with?

Thank you much!

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    $\begingroup$ What do you want to learn about? What's your end goal? $\endgroup$
    – David Roberts ♦
    Commented Apr 17, 2020 at 22:17
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    $\begingroup$ I want to learn about the ways sheaves appear in and connect different areas of mathematics $\endgroup$
    – categoricalimperative
    Commented Apr 17, 2020 at 22:40
  • $\begingroup$ Why not also read other sources, such as some SGA/stacks project, Mac Lane and Moerdijk, or even Bredon's "Sheaf theory" (it's old, but takes a different viewpoint to the alg geom school that took sheaves up shortly after)? $\endgroup$
    – David Roberts ♦
    Commented Apr 18, 2020 at 0:03
  • $\begingroup$ twitter.com/viditnanda/status/1249033158659538945/photo/1 $\endgroup$
    – Praphulla Koushik
    Commented Apr 25, 2020 at 15:07

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"Sheaves on Manifolds" is a good way to learn... well, how sheaves play a role on manifold theory. Especially if you want to compute cohomology of sheaves, and of other functors on derived categories. Beautiful and inspiring mathematics.

But if your aim is "to learn about the ways sheaves appear in and connect different areas of mathematics", you should definitely turn to topos theory and categorical logic.

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  • $\begingroup$ Any prerequisites to start reading topos theory and categorical logic? Can you also share if you have any personal choice for reference for the same.. $\endgroup$
    – Praphulla Koushik
    Commented Apr 24, 2020 at 17:18
  • $\begingroup$ Do you know what a sheaf on a topological space is? I bet you do, since you wanted to read Kashiwara :) what else? Basic category theory (Yoneda lemma, co/limits, adjoints and their properties). First-order logic. Universal algebra. $\endgroup$
    – fosco
    Commented Apr 24, 2020 at 20:51
  • $\begingroup$ I do not know much about First-order logic/Universal algebra. I will read that first.. Thanks.. $\endgroup$
    – Praphulla Koushik
    Commented Apr 25, 2020 at 3:16

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