Weibel HA Exercise 1.5.9

Here's a sketch. The details it leaves to be checked are fairly straightforward, I hope.

Let $g:\text{im}(f)\to C$ be the inclusion map.

There is a short exact sequence of complexes $$0\to\ker(f)[-1]\to\text{cone}(f)\to\text{cone}(g)\to0,$$ which gives a long exact sequence of homology.

The natural map $\text{cone}(f)\to\text{cok}(f)$ factors through $\text{cone}(g)$, with the resulting map $\text{cone}(g)\to\text{cok}(f)$ a quasi-isomorphism.

Why those who dislike the fact that the reals are uncountable always attack Cantor's diagonal proof?

An alternative way to define improper integrals

Compute the integral $\int_0^1\int_0^1\ldots\int_0^1 f(x_1 + x_2 + \ldots + x_n)\,dx_1\,dx_2\ldots dx_n $

Strength of $\sf ZF$+The weak topology on every Banach space is Hausdorff

$f\circ g(x)$ and $g\circ f(x)$ are given; find $f$ and $g$

Quasi-inverse of an equivalence of categories is unique up to unique isomorphism

When does $f(X) = g(X+1)-g(X)$ where $f, g \in \mathbb{C}(X)$?

Use Ramanujan’s method to denest $\sqrt[3]{7\sqrt[3]{20}-1}$ and $\sqrt[3]{7\sqrt[3]{20}-19}$

How many ways to colour a $4 \times 4$ grid using four colours subject to three constraints

Calculating this class number

What is the difference between a Savitzky-Golay filter and LOESS?

SNMP Network traffic difference between ifInOctet and ifHCInOctet