The Clowder Project

On relations:

1. Chapter 6: Relations, Question 6.3.8.1.2, on better characterisations of representably full morphisms in $\textbf{Rel}$. This question also appears as [MO 467527].
2. Chapter 6: Relations, Question 6.3.10.1.2, on better characterisations of corepresentably full morphisms in $\textbf{Rel}$. This question also appears as [MO 467527].
3. Chapter 6: Relations, Question 7.2.1.1.2, seeking a characterisation of which left Kan extensions exist in $\textbf{Rel}$. This question also appears as [MO 461592].
4. Chapter 6: Relations, Question 7.2.1.1.3, seeking an explicit descriptions of left Kan extensions along relations of the form $f^{-1}$ (which always exist in $\textbf{Rel}$). This question also appears as [MO 461592].
5. Chapter 6: Relations, Question 7.2.2.1.2, seeking a characterisation of which left Kan lifts exist in $\textbf{Rel}$. This question also appears as [MO 461592].
6. Chapter 6: Relations, Question 7.2.2.1.3, seeking an explicit descriptions of left Kan lifts along relations of the form $\text{Gr}\webleft (f\webright )$ (which always exist in $\textbf{Rel}$). This question also appears as [MO 461592].

On categories:

1. Chapter 9: Categories, Question 9.6.2.1.3, seeking a better characterisation of necessary and sufficient conditions on $F$ for $F^{*}$ to always be full. This question also appears as [MO 468121].
2. Chapter 9: Categories, Question 9.6.4.1.3, seeking a characterisation of necessary and sufficient conditions on $F$ for $F^{*}$ or $F_{*}$ to be conservative. This question also appears as [MO 468125].
3. Chapter 9: Categories, Question 9.6.5.1.2, seeking a characterisation of necessary and sufficient conditions on $F$ for $F^{*}$ or $F_{*}$ to be essentially injective. This question also appears as [MO 468125].
4. Chapter 9: Categories, Question 9.6.6.1.2, seeking a characterisation of necessary and sufficient conditions on $F$ for $F^{*}$ or $F_{*}$ to be essentially surjective. This question also appears as [MO 468125].
5. Chapter 9: Categories, Question 9.7.1.1.3, , seeking a characterisation of necessary and sufficient conditions on $F$ for $F^{*}$ or $F_{*}$ to be dominant. This question also appears as [MO 468125].
6. Chapter 9: Categories, Question 9.7.2.1.3, seeking a characterisation of necessary and sufficient conditions on $F$ for $F^{*}$ or $F_{*}$ to be monic. This question also appears as [MO 468125].
7. Chapter 9: Categories, Question 9.7.3.1.3, seeking a characterisation of necessary and sufficient conditions on $F$ for $F^{*}$ or $F_{*}$ to be epic. This question also appears as [MO 468125].
8. Chapter 9: Categories, Question 9.7.5.1.5, seeking a characterisation of necessary and sufficient conditions on $F$ for $F^{*}$ or $F_{*}$ to be pseudoepic. This question also appears as [MO 468125].
9. Chapter 9: Categories, Question 9.7.5.1.3, seeking a characterisation of pseudoepic functors. This question also appears as [MO 321971].
10. Chapter 9: Categories, Question 9.7.5.1.4, which asks whether a pseudomonic and pseudoepic functor must necessarily be an equivalence of categories. This question also appears as [MO 468334].
11. Chapter 9: Categories, Question 9.8.4.1.3, seeking a characterisation of functors representably faithful on cores.
12. Chapter 9: Categories, Question 9.8.5.1.3, seeking a characterisation of functors representably full on cores.
13. Chapter 9: Categories, Question 9.8.6.1.3, seeking a characterisation of functors representably fully faithful on cores.
14. Chapter 9: Categories, Question 9.8.7.1.3, seeking a characterisation of functors corepresentably faithful on cores.
15. Chapter 9: Categories, Question 9.8.8.1.3, seeking a characterisation of functors corepresentably full on cores.
16. Chapter 9: Categories, Question 9.8.9.1.3, seeking a characterisation of functors corepresentably fully faithful on cores.