Intereting Posts

No nonconstant coprime polynomials $a(t)$, $b(t)$, $c(t) \in \mathbb{C}$ where $a(t)^3 + b(t)^3 = c(t)^3$.
Covergence test of $\sum_{n\geq 1}{\frac{|\sin n|}{n}}$
What can I guess for this differential equation?
Why is the Cartesian product of a set $A$ and empty set an empty set?
dual cone is closed
Quadruple of Pythagorean triples with same area
Show that $(2+i)$ is a prime ideal
Is the closedness of the image of a Fredholm operator implied by the finiteness of the codimension of its image?
Books to release our inner Ubermensch with calculus?
Binomial Expansion, Taylor Series, and Power Series Connection
General Integral Formula
Are there ways of finding the $n$-th derivative of a function without computing the $(n-1)$-th derivative?
Analytic Continuation of Zeta Function using Bernoulli Numbers
Closed form for definite integral involving Erf and Gaussian?
Why doesn't $(x^a)^b$ always equal $x^{ab}$

Let $\mathcal{A}$ and $\mathcal{B}$ be abelian categories. Suppose $\mathcal{A}$ has enough injectives, and consider a universal (cohomological) $\delta$-functor $T^\bullet$ from $\mathcal{A}$ to $\mathcal{B}$. By the theory of derived functors, we know that that $T^n (A) = 0$ for all injective objects $A$ and all $n \ge 1$ and that $T^n$ is effaceable for $n \ge 1$. But can this be shown directly without invoking derived functors?

- What is the most general category in which exist short exact sequences?
- Derived category and so on
- Computation of the hom-set of a comodule over a coalgebra: $Ext_{E(x)}(k, E(x)) = P(y)$.
- Mitchell's Embedding Theorem for not-necessarily-small categories
- Is a kernel in a full additive subcategory also a kernel in the ambient abelian category?
- The projective model structure on chain complexes
- Example of a non-splitting exact sequence $0 → M → M\oplus N → N → 0$
- When should one learn about $(\infty,1)$-categories?
- Example computation of $\operatorname{Tor_i}{(M,N)}$
- Computing left derived functors from acyclic complexes (not resolutions!)

- A linearly independent, countable dense subset of $l^2(\mathbb{N})$
- Rotation matrix in terms of dot products.
- ELI5: Riemann-integrable vs Lebesgue-integrable
- Fourier transform of a compactly supported function
- Why are K3 surfaces minimal?
- In what sense of “structure” do group homomorphisms “preserve structure”?
- What books should I get to self study beyond Calculus for someone about to start undergrad mathematics?
- Definition of $d (P (x ,y )dx)$
- with inequality $\frac{y}{xy+2y+1}+\frac{z}{yz+2z+1}+\frac{x}{zx+2x+1}\le\frac{3}{4}$
- Do Symmetric Games with Nash Equilibria always have a symmetric Equilbrium?
- Proving the closed unit ball of a Hilbert space is weakly sequentially compact
- If N and every subgroup of N is normal in G then G/N is abelian .
- Why does Van Kampen Theorem fail for the Hawaiian earring space?
- infinite disceret subspace
- Example of a continuous function that is not measurable