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Thought I would offer up a new toy for you guys to play with: apply the Grothendieck construction to the functor from sets to categories obtained by composing a contravariant hom 2-functor (for some fixed category C) with the functor taking sets to their corresponding discrete categories. Objects in the entire category for the induced bundle are like sets, but rather than bags of structureless points, they are bags of objects living in C. A morphism is a function on the underlying set, but where each assignment f(x)=y is actually a morphism x—>y from C. Notice that we can embed C into this new category by the obvious assignment taking c to {c}.
Also of interest: if you decategorify this entire setup, you obtain a process for taking a set S to a new set; the new set is just S+{*}. This is in fact part of the maybe monad, so in a sense my construction looks like a categorified maybe monad.
Observe how similar the category of groupoids is to the category obtained above by applying the construction to the category of groups.
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>>8393766
Lol what?
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>>8393782
brainlet detected lol
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>>8393782
Sorry if my description is lacking. Apply the construction to the functor I gave and you will see!
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>>8393766
Is the picture indicative of a certain source of mathematical creativity of yours?
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>>8393806
Haha, nah, just something cool that I saved for the next time I trip.
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>>8393806
Oh, I misread your post. Yes, it is!
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why would I care about metamathematics when I can do mathematics?
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>>8393812
Interesting comment my friend. For me, I am doing metamathematics because it is the best place to express my philosophical ventures; it has the scope of philosophy and the rigour of mathematics, making it an ideal place to roam.
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>>8393809
So you'd say the experience doesn't commonly lend you easy insights into your mathematical interests? No geometric synaesthesia with those fancy categorical structures, etc?
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>>8393815
philosophy is for gaylords, lol
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>>8393819
I have mild synesthesia already, and it seems LSD does not affect that process very much. Generally I get no insights until I am done tripping and have a chance to evaluate my thoughts. I have only done a tab at a time, so perhaps a larger dose would lead to more pronounced visual phenomena.
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