Timeline for Is the category of small categories locally presentable?
Current License: CC BY-SA 4.0
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| Jun 14, 2023 at 17:17 | history | edited | Todd Trimble | CC BY-SA 4.0 |
improved display line LaTex
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| Dec 31, 2011 at 13:41 | comment | added | Todd Trimble | @Martin: The main difference to monoids is that a coequalizer in $Cat$ which identifies different objects can introduce new loops. One can witness this behavior by considering the coequalizer of the two object inclusions $1 \to 2$ into the generic arrow; the coequalizer is then $\mathbb{N}$ seen as a monoid. This doesn't come up in $Mon$. It's not that coequalizers in $Cat$ are ferociously complicated, but they are a little fiddly because of looping, and the sort of niceties available for $Mon$ (e.g., $U: Mon \to Set$ preserves reflexive coequalizers) are not quite as nice here. | |
| Dec 31, 2011 at 11:29 | comment | added | Martin Brandenburg | I don't think that colimits of categories are really complicated when one has understood colimits of monoids (since categories are just monoidoids). On the other hand, 2-colimits are more complicated. | |
| Dec 28, 2011 at 21:14 | vote | accept | Fernando Muro | ||
| Dec 28, 2011 at 20:52 | history | answered | Todd Trimble | CC BY-SA 3.0 |