active · last success 2026-08-05 03:33
Looking at Nat |Id,Id| for the category of M-Sets when M is a monoid and contrasting this with Nat |U,U| where U: M-Set to Set is the forgetful functor.
A couple more examples of ends. Firstly, otaining Nat |F,G| as an end. Secondly, a baby example of Tannakian reconstruction: if M is a monoid in Set, and U is the forgetful functor from M-Set to Set then Nat |U,U| = M.
Further explanation of the Yoneda embedding (including calling it that, but not yet proving it's an embedding), checking naturality for H_f.
Definition of representable functors and the Yoneda embedding (though without calling it the Yoneda embedding yet)
Definition of comma categories D over and under F for a functor F, and F over and under G for functors F and G with the same target category
Definition of coequaliser, examples in Set: coequalisers can be constructed as equivalence relations, and equivalence relations can be expressed as coequalisers
