2
votes
2answers
55 views

Epic-monic factorisation in $\mathbf{Set}$.

I'm stuck on Exercise 5.2.1 of Goldblatt's "Topoi: A Categorial Analysis of Logic": Given a function $f:A\to B$, if $h\circ g: A\twoheadrightarrow C\rightarrowtail B$ and $h'\circ g': ...
0
votes
1answer
34 views

Left & right adjoints in the context of complete lattices.

This is a follow-up question from this question of mine. In the same paper as the one mentioned in my previous post, it's stated that In the context of complete lattices, a monotone map has a ...
2
votes
0answers
127 views

Prove the FHHF theorem using as much abstract non-sense as possible

This is my second attempt to solve exercise 1.6H from Vakil: Assume $F$ is a covariant right-exact functor and show that we get a map $HF^i \rightarrow H^iF$. Attempt to a solution: Apply $F$ to the ...
5
votes
1answer
349 views

Excessive use of the Yoneda lemma

In a MathOverflow thread on "nuking mosquitos", Andrej Bauer offered the following proof: If two elements in a poset have the same lower bounds then they are equal by Yoneda lemma. I understand ...
4
votes
1answer
290 views

Possible mistake in Krause's “Localization Theory”

I'm a little confused about a proof in this note by H. Krause; see page 12, Prop. 3.5.1. Can you explain me how the $\beta_i$'s are determined? I can't catch how to choose them in order to coequalize ...