Timeline for Group Presentation - Categorical Interpretation
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 5, 2017 at 13:44 | comment | added | Musa Al-hassy | @DerekElkins Thanks for the clarification, I feel that relators aren't well-known but glad to see them showing up! I sense that you've read some works of Fokkinga and Backhouse. Thanks for the blog link ^_^ | |
| Apr 5, 2017 at 3:52 | comment | added | Derek Elkins left SE | @CWL You may find my blog article interesting, or at least the references it cites, which I recommend, though "Basic Concepts of Enriched Category Theory" definitely isn't aimed at beginners. Depending on your background, you may also find this article interesting depending on your background, though it's definitely... non-traditional. | |
| Apr 4, 2017 at 14:58 | comment | added | Bryan Shih | Thanks a lot Derek, I believe I still have a lot to learn. i.e. limits, colimits, and adjoints etc... I will come back and review your post once I have better understanding :) | |
| Apr 4, 2017 at 14:13 | comment | added | Derek Elkins left SE | @MusaAl-hassy $\mathbf{Grp}(-,G)$ is contravariant and $R_i$ is explicitly stated as being $\mathbb{Z}\to FX$. I definitely am ambiguously referring to $R_i$ as "relations" at the beginning. "Relator" would be a better word. I'll probably expand how the coequalizer leads to the quotient and clean up the wording in that section later. Arguably, the $\bar R_i$ are "really" what the relators are and coding them up as group homomorphisms is just so I can present the quotient as a coequalizer in $\mathbf{Grp}$. | |
| Apr 4, 2017 at 13:44 | comment | added | Musa Al-hassy | Perhaps expand on the type of $R_i$; are they "relations" or "functions" or what. Making clear what mathematical creature they are may make it clear how we jump to: $\mathbf{Grp}(R_i,G):\mathbf{Grp}(FX,G)\to\mathbf{Grp}(\mathbb{Z},G)$. Indeed, this latter item suggests, due to Yoneda, that $R_i : F\, X \to \mathbb{Z}$, and is that what is intended? If so, perhaps clarify and elaborate, as the asker claims to be "new" and you state you want to go from abstract to concrete ;) | |
| Apr 4, 2017 at 13:30 | comment | added | Musa Al-hassy | The importance of Skolemisation (in the categorical setting) cannot be overstated! | |
| Apr 4, 2017 at 10:26 | history | answered | Derek Elkins left SE | CC BY-SA 3.0 |