@BillDubuque Might well be. Unfortunately, I never grokked quadratic reciprocity well enough to understand why higher analogues were such a holy grail. As a stepping stone to discrete logarithms somehow?
No matter how I hard I try I always forget this formula $\displaystyle\prod_{\alpha < \kappa} \sum_{i \in I_{\alpha} } u_{\alpha, i}= \sum_{f \in \prod_{\alpha < \kappa} I_\alpha } \prod_{\alpha < \kappa} u_{\alpha, f(\alpha) }$.
While being a teenager I for a limited amount of time was transformed into a superman with computer brain. Read this chapter of my book about my transformatiom.
Oh. An $Ab$-category is not the same as an Abelian category!? It's the same as a pre-additive category which is the same as a ringoid which is the same as an $Ab$-enriched category?
this is incredibly frustrating, I haven o idea what I am doing wrong on this problem I have done it 6 times now. If I am making u substitution for integrating can I just ignore the bounds until the end and the plug back in all my substitutions correctly and get a correct answer?
I hate how there are so many ways to do an integral right but only one or two that are the right answer even though I am doing the math right the answer is wrong somehow
I think I'll go with pre-additive to mean a category where the sets of morphisms are Abelian groups (I assume that means addition of morphisms) and such that concatenation is bilinear.
I have been doing this proble mfor over an hour, I have went though it half a dozen times and I can not find any mistakes, I have done it 3 different ways
This seems pretty simple to me but I can't get it.
$$\int \sin^2 x \cos^2 x dx$$
$$\int (1-\cos^2 x) \cos^2 x dx$$
I know there is a rule in my book (with little explanation) that tells me when I had an odd and an even degree on two trig functions I should split the odd and convert it to an id...
Hm... All categories I can think of are pre-additive. Surely, Set is pre-additive and so is Mod. Ah, Grp is not. Only if it's the category of Abelian groups. I see.
There exists an abelian category whose set of objects is $\mathbb{N}$, but it's basically a funny way of talking about $\textbf{Vect}^\textrm{f.d.}_k$.
Matt n. a finite set may be thought of as a category. the points in the set are jst little dots but they are the objects in the category and have no internal structure
I have wasted so much time on this one problem and I only have 2 days left to study, I feel like I should just skip this problem because I can't ask it here anymore
A category $\mathbb{C}$ comprises the following data: a set $C_0$, a set $C_1$, a map $s : C_0 \to C_1$, a map $t : C_0 \to C_1$, a map $\rho : C_0 \to C_1$, and a map $\tau : C_2 \to C_1$, where $C_2 = \{ (g, f) \in C_1 \times C_1 : s(g) = t(f) \}$, and all these are required to satisfy various axioms.
We require $s(\rho(x)) = t(\rho(x)) = x$: $\rho : C_0 \to C_1$ is the witness of the reflexivity of this graph; in other words, $\rho(x)$ is a distinguished edge from $x$ to $x$.
This seems pretty simple to me but I can't get it.
$$\int \sin^2 x \cos^2 x dx$$
$$\int (1-\cos^2 x) \cos^2 x dx$$
I know there is a rule in my book (with little explanation) that tells me when I had an odd and an even degree on two trig functions I should split the odd and convert it to an id...
