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user 2273
7
votes
Adjusting the definition of a well-powered category to category theory with universes: size ...
One simple way is to read the traditional definitions (à la Grothendieck, etc) but replacing existence conditions with chosen structure:
A category $C$ is $U$-locally-small if it is equipped with a …
- 21.3k
3
votes
Accepted
Equivalence of the two definitions of k-compactness/k-presentability
The definitions are equivalent as stands; no extra conditions (eg majorants for infinite sets of factorisations) are needed. This is essentially because colimits in $\mathbf{Sets}$ are computed finit …
- 21.3k