While CatDat already has a couple of well-known categories, some are currently missing. Here are some suggestions. Done categories are moved to the bottom.
| Notation |
Category |
Links |
Done |
| $Grp_{fg}$ |
finitely-generated groups |
|
❌ |
| $Grp_{fp}$ |
finitely-presented groups |
|
❌ |
| $Ab_{c}$ |
countable abelian groups |
|
❌ |
| $grMod_R$ |
Graded modules |
|
❌ |
| $CGWH$ |
compactly generated weak Hausdorff spaces |
|
❌ |
| $hTop$ |
Homotopy category of Top |
|
❌ |
| $TopGrp$ |
Topological groups |
|
❌ |
| $LCH$ |
locally compact hausdorff spaces |
|
❌ |
| $Ban_c$ |
Banach spaces with continuous linear maps |
MSE/1424777 |
❌ |
| $TopVect$ |
Topological vector spaces |
|
❌ |
| $NormVect$ |
Normed vector spaces |
WIP, #127 |
❌ |
| $CompMet$ |
Compact metric spaces |
MSE |
❌ |
| $C^*-Alg$ |
C*-algebras |
|
❌ |
| $LawMet$ |
Lawvere metric spaces |
|
❌ |
| $Mod(O_X)$ |
Modules over a sheaf of rings |
|
❌ |
| $RS$ |
Ringed spaces |
|
❌ |
| $Qcoh(X)$ |
Quasi-coherent sheaves |
Thesis |
❌ |
| $Alg(O_X)$ |
Algebras over a sheaf of rings |
|
❌ |
| $Unif$ |
uniform spaces* |
MO |
❌ |
| $Stoch$ |
measurable spaces with Markov kernels |
nlab |
❌ |
| $\Pi_1(X)$ |
fundamental groupoid of a (specific) space, say $X = S^1$
|
|
❌ |
| $Born$ |
bornological sets / spaces |
|
❌ |
| $Grp_{c}$ |
countable groups |
|
✅ |
| $CompHaus$ |
Compact Hausdorff spaces |
|
✅ |
| $Haus$ |
Hausdorff spaces |
|
✅ |
| $\Delta$ |
Simplex category |
|
✅ |
| $SemiGrp$ |
semigroups |
|
✅ |
| $TorsAb$ |
torsion abelian groups |
|
✅ |
*either with continuous or uniform maps, not sure yet
Also:
- Add the categories from https://math.stackexchange.com/questions/4481902/locally-presentable-vs-compactly-presentable-categories
- Add the categories from https://mathoverflow.net/questions/258269/cocomplete-topoi-that-are-not-grothendieck
- Add the categories from https://math.stackexchange.com/questions/2864916/ (two locally cartesian closed categories that are not cartesian closed)
IMPORTANT. Adding these categories to the categories table is easy, but not sufficient, since (see CONTRIBUTING.md) one should also try to fill in the properties and non-properties (in case they are not deduced already). So this is actually a quite big task. Maybe one can make one commit (or PR) per category.
While CatDat already has a couple of well-known categories, some are currently missing. Here are some suggestions. Done categories are moved to the bottom.
*either with continuous or uniform maps, not sure yet
Also:
IMPORTANT. Adding these categories to the categories table is easy, but not sufficient, since (see
CONTRIBUTING.md) one should also try to fill in the properties and non-properties (in case they are not deduced already). So this is actually a quite big task. Maybe one can make one commit (or PR) per category.