>>12009058I'm the original guys, mapping to cosets fucks welldefinedness up the ass, probably what the other guy was trying to say
Taking cosets would have 1 and 8 map to the same object in DoW, so 1<7<8 => M < S < M which is fuck shit we were trying to avoid
The right construction is just taking {1,2,...7} as the objects and taking the morphisms as the restriction of the one on Z^2
But even then you have a choice to define what the first day of the week is
Say you choose to start the week on Sunday and i choose Monday
Then by comparing our categories Sun < Mon in yours, and Mon < Sun in mine
But this is just because i took a different representative for Sun, i took 8 = Sunday, if the rest of our days match up
Also this is just taking a specific run of 7 days as a category, so i find it inappropriate to call it "The Days of the Week" category
its just "The Days of A Week"
in conclusion, fuck cosets, all my homies choose specific representatives and then redefine their operations from that new set.
