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Questions designed to generate a "big list" of certain results, examples, conjectures, etc. via many individual answers, each contributing one or a few instances. Such a question should typically be in Community Wiki mode (CW); after asking, please, flag for moderators attention requesting the question to be made CW.
2
votes
Graphical representation of mathematical structures (in the spirit of unified modeling langu...
One could consider UML as a kind of "front end" for category theory. For example, a basic database schema is just a category (and a more interesting database schema is a sketch).
So if UML is just …
6
votes
Big list of comonads
For any monoid $(M,e,*)$ in $\mathsf{Set}$ there is a corresponding comonad $y^M$ on $\mathsf{Set}$. It sends a set $A$ to the set of morphisms into $A$ from $M$,
$$
A\mapsto A^M.
$$
Note that $y=y^1$ …