What is the name for a category defined by a finite commutative diagram?
Maybe category "induced" by a commutative diagram? or category "defined" by a commutative diagram?
Also, what is the exact definition of this intuitively clean concept?
2026-04-13 23:48:46.1776124126
Category defined by a finite commutative diagram
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It is usually called the free category on (over) the diagram, but the term 'induced by' is also clear.
We can formalize abstract diagrams as directed graphs (i.e. quivers) with a set of commutativity conditions, which are just pairs of parallel paths.
Then we have the usual free-forgetful adjunction between these abstract diagrams and categories.