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Questions tagged [representable-functor]

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3
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1answer
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Equivalence of two definitions of local functors

All my functors are from commutative rings to sets. I've seen two different definitions of a local functor. In one definition we say $X$ is local if whenever $Y$ is a functor with open cover $Y_i$ ...
2
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1answer
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checking the functor $\texttt{Nil}_n$ is represented by $(\mathbb{Z}[x]/(x^n), \tau_R)$

This is the continuation of another question I did some days ago. Here. I have been working on it and I would like to know if my try to prove it is right or not. I would appreciate a lot any feedback ...
0
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1answer
97 views

Given the adjunction morphisms $\epsilon, \eta$, then $(\eta \circ L) \circ(L\circ \epsilon) = \text{id}_L$ is easy to check.

Given the adjunction morphisms $\epsilon, \eta$, then $(\eta \circ L) \circ(L\circ \epsilon) = \text{id}_L$ is easy to check. This is from page 29 of "categories and sheaves". I have a major ...