An "inverse limit" is a limit, a "direct limit" is a colimit, and I think I'm going to commit a crime against whoever came up with that.
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Replying to @BiCapitalize
Yeah... i really like the terms projective and injective limits. I can never remember which is which. At least projective/injective tells you which way the arrows are going!
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Replying to @pitopos @BiCapitalize
I remember this by the fact that projective starts with p and the p-adics are like my only example of a projective limit
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Replying to @knotbrendan @BiCapitalize
Oh i mean i can't remember which is the inverse and which is direct! Projective and Injective are perfectly clear terms to me.
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Replying to @pitopos @BiCapitalize
-->-->-->-->--> direct limit inverse limit -->-->-->-->--> The direct limit is being pointed at, sitting in front of all the objects in your diagram, while the inverse limit is "behind" everything.
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this is another one of those things where i can only remember it by remembering that it's the opposite way around to how i always think it should be
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The direct limit is direct: if you see -->-->-->--> you just follow the damned arrows to find the direct limit. Inverse means you *don't* follow the arrows - you go the other way.
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I just want to share my favourite/only category theory mnemonic: the only way I can reliably remember which functors are left adjoints and which are right adjoints is that forgetful functors are right adjoints because of the EU legal phrase "right to be forgotten".
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Replying to @increpare @johncarlosbaez and
I would like to start a thread: « how would you call a right adjoint and a left adjoint if you could decide a new name? »
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