active · last success 2026-06-19 22:12
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.
The first example of an end. Natural transformations of the identity as the end of the hom functor.
A first look at generalizing the notion of natural transformation to the enriched setting.
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 slice categories C/X and X/C, products in C/X as pullbacks in C
Definition of coequaliser, examples in Set: coequalisers can be constructed as equivalence relations, and equivalence relations can be expressed as coequalisers
The definition of the pull-back and its right adjoint for bundles over sets.
