Is there a difference between the Quotient category and a categorical schema?

Bruno Gavranović

In Seven sketches, categorical schemas are talked about a lot. They're given by a graph and a path equivalence relation on that graph. It seems very much like the construction of the quotient category (https://en.wikipedia.org/wiki/Quotient_category), which identifies sets of morphisms as well.

Is there perhaps a subtle difference between these two? Seven sketches doesn't seem to mention quotient categories at any point

Bruno Gavranović

There is also a phrase "finitely-presented category" mentioned in Seven sketches, which seems like a very similar thing. I'm wondering if there are any subtle differences

Pierre Prado

"formally" word in wikepedia points a difference in my opinion..

Pierre Prado

https://ncatlab.org/nlab/show/quotient+category

strict localization...

Bruno Gavranović

Do you mean the "Formally, it is a quotient object in the category of (small) categories, analogous to a quotient group or quotient space, but in the categorical setting." sentence? Doesn't a path equivalence relation on Free(G) exactly the congruence R they talk about on the Wikipedia page? Can't we define the quotient category Free(G)/~ in very much the same way, such that there's a quotient functor Q which equates certain paths?

Pierre Prado

yes this "formally"...regarding Free(G) i dont know if you are right or not..