@themattsimpson @sarahdoingthing A category contains all the objects of a particular kind and all the functions between them.
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Replying to @St_Rev
@themattsimpson
@sarahdoingthing So Set contains all sets and all functions, Top contains all topological spaces & continuous maps, etc.1 reply 0 retweets 1 like -
Replying to @St_Rev
@themattsimpson
@sarahdoingthing Now a *functor* is a kind of function that goes from one category to another. Context switching.1 reply 0 retweets 2 likes -
Replying to @St_Rev
@themattsimpson
@sarahdoingthing Functors turn questions about topology into questions about algebra, and so on. "The light's better here"2 replies 1 retweet 4 likes -
Replying to @sarahdoingthing
@St_Rev @themattsimpson (once you complete the portage)1 reply 0 retweets 1 like -
Replying to @sarahdoingthing
@sarahdoingthing @themattsimpson Well, going one way is frequently easy, lifting back to the original problem not so much.1 reply 0 retweets 0 likes -
Replying to @St_Rev
@sarahdoingthing Here's an example: the idea of 'invariants'. Say you have two colossally tangled masses of string, and you want to know...1 reply 0 retweets 1 like -
Replying to @St_Rev
@sarahdoingthing ...if they're the 'same knot', topologically. This is super hard! But there are things called knot invariants.1 reply 0 retweets 2 likes -
Replying to @St_Rev
@sarahdoingthing A knot invariant is a recipe for turning a horribly complicated object (a tangled ball of string) into a simple one...2 replies 0 retweets 1 like
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