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': ...
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 ...
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 ...
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 ...
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 ...