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

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

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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

Comment Source: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
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"formally" word in wikepedia points a difference in my opinion..

Comment Source:"formally" word in wikepedia points a difference in my opinion..
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Comment Source:https://ncatlab.org/nlab/show/quotient+category strict localization...
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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?

Comment Source: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?
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edited January 22

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

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