Category theory MOC

Free category

Free categories are the free objects in Category of small categories, cat forming the left adjoint to the forgetful functor to the Underlying quiver

The free category is constructed by considering all composable words, called paths, as morphisms.

Universal property

If is a Small category with Underlying quiver and is a quiver homomorphism then there exists a unique adjunct such that the following diagram commutes:

https://q.uiver.app/#q=WzAsNSxbMCwwLCIgQ1xcR2FtbWEiXSxbMCwyLCJcXG1hdGhzZiBEIl0sWzIsMCwiVUNcXEdhbW1hIl0sWzIsMiwiVVxcbWF0aHNmIEQiXSxbNCwwLCJcXEdhbW1hIl0sWzAsMSwiXFxleGlzdHMhIGciLDIseyJzdHlsZSI6eyJib2R5Ijp7Im5hbWUiOiJkYXNoZWQifX19XSxbNCwyLCJcXGV0YV9DIiwyXSxbNCwzLCJmIl0sWzIsMywiVWciLDJdXQ==


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