Recently the category theory started to appear more frequently in the paper readings. From the Wikipedia page Timeline of category theory and related mathematics it seemed that the category theory had the applications in the string theory in various places. For example, it showed up in the discussion concerning the topological structures.

However, unlike the group theory and the set theory, the category theory was not usually offered in standard lectures, and less so for the mathematical physics. The Wikipedia page explained the entities of the Category theory (objects, morphisms, and binary operation), which was understandable, but the webpage did not provide the examples of the applications.

There were some useful references for the category theory from the math exchange:

1. https://math.stackexchange.com/questions/2630894/recent-sets-of-notes-newly-available-online-books-on-category-theory

2. Implementing Category Theory in General Relativity

3. https://math.stackexchange.com/questions/370/good-books-and-lecture-notes-about-category-theory?rq=1

but it's unclear how the category theory were frequently used in the string theory, i.e. in the abstract algebra, there's lie groups, the generators etc. in the set theory it was even more commonly accepted as a standard tool, but why the category were so useful? is there a "special string category" that's particular useful in the string theory?

How was the category theory implemented in the string theory, and were there some the references or lecture notes for the category theory in the string theory?

Recently category theory started to appear more frequently in my paper readings. From the Wikipedia page Timeline of category theory and related mathematics it seemed that category theory had applications in string theory in various places. For example, it showed up in discussions concerning topological structures.

However, unlike group theory and set theory, category theory was not usually offered in standard lectures, and less so for mathematical physics. The Wikipedia page explained the entities of category theory (objects, morphisms, and binary operation), which was understandable, but the webpage did not provide the examples of applications.

There are some useful references for category theory from the math exchange:

1. https://math.stackexchange.com/questions/2630894/recent-sets-of-notes-newly-available-online-books-on-category-theory

2. Implementing Category Theory in General Relativity

3. https://math.stackexchange.com/questions/370/good-books-and-lecture-notes-about-category-theory?rq=1

but it's unclear to me how category theory is frequently used in the string theory, i.e. in abstract algebra, there's Lie groups, generators etc. Set theory is even more commonly accepted as a standard tool, but why are categories so useful? Is there a "special string category" that's particularly useful in string theory?

How is category theory implemented in the string theory, and are there some references or lecture notes for category theory in string theory?