Question

Show that $\lim$ is a right adjoint to the constant functor

score 625 · Answer 1 · 2026-03-25 04:57:30

Show that $\lim$ is a right adjoint to the constant functor

Published on 25 Mar 2026 - 4:57

score 46 · Answer 2 · 2026-03-25 05:10:02

Limit of $h_{\mathcal C} \circ F$ for $F: I \to \mathcal C$ exists in $\text{Func}(\mathcal C^\text{op}, \text{Set)}$ and is $\text{Hom}(\_,\lim F)$.

score 114 · Answer 3 · 2026-03-26 15:08:43

114

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score 105 · Answer 5 · 2018-10-22 21:45:22

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List Question

Show that $\lim$ is a right adjoint to the constant functor

Limit of $h_{\mathcal C} \circ F$ for $F: I \to \mathcal C$ exists in $\text{Func}(\mathcal C^\text{op}, \text{Set)}$ and is $\text{Hom}(\_,\lim F)$.

Category theory - Prove that $\operatorname{Hom}$ preserves representations for quasi-inverse functors

Is the functor that assigns to an algebra its algebraic group of units fully faithful?

Operations between subgroups in a free product of groups

How to prove naturality in $c$ of $\text{Hom}_D(Fc, d) \simeq \text{Hom}_C(c, Ud)$ given adjunction $(F, U)$?

Can a class contain other (proper) classes?

exponentiation structure-preserving maps

In category theory, what does the $\otimes$ symbol mean?

Help tracking down an article in which "implementations of functions" were defined via "iterators"?

Homotopy like a path in Hom(X,Y)

$Set$, $Set^{op}$, categorical properties, and proving why these categories aren't isomorphic.

The category of relations $Rel$ and proving it is isomorphic to its opposite

Question on a specific pullback.

Simple example of product not preserving coequaliser in $\mathbf{Top}$

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