I love farming
其实主要是为了看懂nominal approach to psl 和各种用sheaves做semantics的邪教玩意 johnli他们2025 Fall要在NEU开个课 主要用topos institute的邪教书 Seven Sketches in Compositionality 假如只是想读topos/sheaves 其实可以直接看chap 7 Topos Institute那帮子人还在MIT用这个教材开过两次课 [2019] [2018] 某种程度上（至少从seven sketches的角度）fixing a topological space that give you a topos is kinda like the kripke semantics in modal logic. So the set of worlds in kripke semantics is kinda like the topological space, and the inclusions of open sets are kinda like world relations.
Daniel Murfet (of course) 照着(?) MM 开过一门课 完整的recording甚至在b站。。。
这个课的大纲其实每一章大体讲得挺清楚的 （最全的recording居然在b站。。。）
惊人的比较完整的课 [youtube playlist] [site]
Subobject Classifier for the category of graphs
Seven Sketches 的 Example 7.54 给了挺好的intuition 尤其是第二段 不过somehow 可以用Yoneda Lemma去找 $\Omega$（我完全不懂。。）
ds其实讲过。。。我自己的somehow you get into a three-valued logic situation
这里有提及 Awodey Example 7.17具体说了how $Graphs = Set^\Gamma$ where $\Gamma$ is the category with two objects and two(four) arrows between them.
Kripke-Joyal Semantics
Seems like there’s a way to introduce it without going thru Grothendieck Topology?
Alex Simpson gave a speed-run tutorial at LICS
(How related is this to the usual Kripke Semantics we give in modal logic in a typical philosophical logic class?)
Grothendieck Topology
Make sense of this point…
A grothendieck topology kind of lets you preserve some colimits of C (in the sense of the Yoneda embedding of C is the free cocompletion (as it obliterates all colimits in C)