It looks like you're new here. If you want to get involved, click one of these buttons!

- All Categories 2.2K
- Applied Category Theory Course 353
- Applied Category Theory Seminar 4
- Exercises 149
- Discussion Groups 49
- How to Use MathJax 15
- Chat 480
- Azimuth Code Project 108
- News and Information 145
- Azimuth Blog 149
- Azimuth Forum 29
- Azimuth Project 189
- - Strategy 108
- - Conventions and Policies 21
- - Questions 43
- Azimuth Wiki 711
- - Latest Changes 701
- - - Action 14
- - - Biodiversity 8
- - - Books 2
- - - Carbon 9
- - - Computational methods 38
- - - Climate 53
- - - Earth science 23
- - - Ecology 43
- - - Energy 29
- - - Experiments 30
- - - Geoengineering 0
- - - Mathematical methods 69
- - - Meta 9
- - - Methodology 16
- - - Natural resources 7
- - - Oceans 4
- - - Organizations 34
- - - People 6
- - - Publishing 4
- - - Reports 3
- - - Software 21
- - - Statistical methods 2
- - - Sustainability 4
- - - Things to do 2
- - - Visualisation 1
- General 39

Options

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

## Comments

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

`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`

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

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

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

strict localization...

`https://ncatlab.org/nlab/show/quotient+category strict localization...`

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?

`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?`

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

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