/sci/ - Science & Math

>>11888555
>>11888341
WHAT

>>11773200
>Also I assume it's chill for me (an undergrad 50% done) to sit in on one of the OATS things tomorrow?
Ah merci for reminding me to remind! Have you been on any of them yet? You don't have to show yourself, you don't have to say anything. You can just listen and watch.

8½ hours till
https://sites.google.com/view/nialltaggartmath/oats
>Kathryn Hess (EPFL)
>Title: Calculus from comonads
>Abstract: (Joint work with Brenda Johnson.) The many theories of "calculus" introduced in algebraic topology over the past couple of decades--e.g., Goodwillie's calculus of homotopy functors, the Goodwillie-Weiss manifold calculus, the orthogonal calculus, and the Johnson-McCarthy cotriple calculus--all have a similar flavor, though the objects studied and exact methods applied are not the same. We have constructed a relatively simple category-theoretic machine for producing towers of functors from a small category into a simplicial model category, determined conditions under which such tower-building machines constitute a calculus, and showed that this framework encompasses certain well known calculi, as well as providing new classes of examples. The cogs and gears of our machine are cubical diagrams of reflective subcategories and the comonads they naturally give rise to.
>In this talk, I will assume no familiarity with comonads and only basic knowledge of simplicial model categories.

if I started going through a pretty basic maths textbook (specifically Elements of Abstract and Linear Algebra by Connell), which doesn't have an answer key for the proofs, would /mg/ let me post my proofs here to be critiqued or would you bully me and tell me to stop spamming?

When I was learning proofs, I recall my professor telling me that
[math] P(n-1) \Rightarrow P(n) [/math]
was a better or more robust or more educated way to do induction proofs than
[math] P(n) \Rightarrow P(n+1) [/math]

but I don't remember how he justified that. Can anybody provide input, re: how that might be the case?