@themattsimpson @sarahdoingthing So Set contains all sets and all functions, Top contains all topological spaces & continuous maps, etc.
@themattsimpson @sarahdoingthing A category contains all the objects of a particular kind and all the functions between them.
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@themattsimpson
@sarahdoingthing Now a *functor* is a kind of function that goes from one category to another. Context switching. -
@themattsimpson
@sarahdoingthing Functors turn questions about topology into questions about algebra, and so on. "The light's better here" -
@St_Rev @themattsimpson it seems like the hard part is showing you're on the "same river" as before -
@St_Rev @themattsimpson (once you complete the portage) -
@sarahdoingthing @themattsimpson Well, going one way is frequently easy, lifting back to the original problem not so much. -
@sarahdoingthing Here's an example: the idea of 'invariants'. Say you have two colossally tangled masses of string, and you want to know... -
@sarahdoingthing ...if they're the 'same knot', topologically. This is super hard! But there are things called knot invariants. - 2 more replies
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. Banned in Sweden. SubGenius, Zhuangist, white-hat troll. Defrocked mathematician. Brain problems.