That was my niche in grad school. I authored a paper proving that the CW-complexes in the category of small categories under the Joyal-Tierney model structure are exactly the groupoids. I never came up with a reason why anyone should care, but at least it was fun.
![And my brain said "no." [KB Comics]](https://slrpnk.net/pictrs/image/859f9670-1bac-4670-a82e-db5eb229f4e7.png){kind=link}
That was my niche in grad school. I authored a paper proving that the CW-complexes in the category of small categories under the Joyal-Tierney model structure are exactly the groupoids. I never came up with a reason why anyone should care, but at least it was fun.
That looks like gobbledygook to me, and I wanna get all up in dat good good gook.