Mnemonics for remembering which functor is left and which is right in an #adjunction :

When two categories are equivalent, you can go from the first category to the second one and then go back.

Imagine that the "first" category is on the left and the second one is on the right.

Then, an adjunction is when you can still go from left to right, using the right-adjoint functor G (AKA "ground" or the forgetful functor) because this functor is not lossy, but you cannot go back from right to left, because the left-adjoint functor F (AKA the free functor) is lossy.

#categorytheory

Reading #adjunction tutorials reminds me the main way that most teaching materials screw up: they *start with the definition* and then *follow with examples*. In reality, the way we learn, the way we discover things always begins with an instance. Definitions come second.

Computational Category Theory
(2022) : D.E Rydeheard and R.M Burstall
url: https://www.cs.man.ac.uk/~david/categories/
#adjunction #category_theory #functional_programming #functors #standard_ML #toposes #unification
#my_bibtex