# Tagged Questions

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### Map induced by localization on categories

I have been doing some reading in Hartshorne's Algebraic Geometry on derived functors and subsequent results in cohomology. Given $A$ an abelian category of groups, I have seen that the map ...
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### How to get used to commutative diagrams? (the case of products).

I've returned to Aluffi's book (after getting the basics of groups from Herstein's) and I hit the same brick wall that made me put it aside. My general problem is this: I can't seem to get used to ...
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### Advice regarding best-practice mathematics / categorial logic.

A good heuristic is: If it doesn't cost anything, generalize. In particular, if we have a theorem, and a proof thereof, then we ought to look for a maximal generalization of this theorem, ...
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### Lawvere theories: an equivalence.

I'm having trouble understanding Lawvere theories (as defined below). Definition: A Lawvere Theory is a category $\mathcal{L}$ with finite products and with a distinguished object $A$ such that ...
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### How much Category theory one must learn?

I have learnt very basic category theory (up to Yoneda lemma from Hungerford's Algebra text). My question is how much category theory should every Mathematics student who is not planning to specialize ...
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### Opposite category functor

I need some confirmation: is the opposite category transformation always a functor? Also, isn't it always the case that $C^{\text{op}} = C$, since the the way we label an arrow does not matter?
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### Yoneda Lemma Exercises

Can you please suggest some (relatively simple) exercises to practice the use of the Yoneda Lemma? Harder exercises are welcome too, but I would like to start with simpler ones. The answers to this ...
### How to prove that untyped $\lambda$ and simply typed $\lambda$ are of diferent expressive powers
How to prove that untyped $\lambda$ and simply typed $\lambda$ are of diferent expressive powers, using category theory? I'm just getting to grips with the basic ideas of category theory, and I'm ...