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I believe that's called the Milgram bar construction: R.J. Milgram, The bar construction and abelian $H$-spaces, Illinois J. Math. 11 (1967), 242-250.

Just yesterday I was looking at Clark Barwick's 121 Exercises on Locally Compact Abelian Groups: An Invitation to Harmonic Analysis. The opening sentence is "This is a collection of challenging exerci …

I will recount the more general statement of linear independence of characters, given in Lang's Algebra book, and credited to Artin. Let $G$ be a group, and $K$ a field. Then distinct homomorphisms $\ …

Conway had an analysis of the notorious Steiner-Lehmus theorem, arguing that no "equality-chasing proof" is possible. MO user Timothy Chow initiated a discussion about Conway's analysis on the FOM lis …

Converting Dimitri Chikhladze's comment to an answer: A "cocategory of object in $\mathsf{CAlg}_R$" is the "commutative case of bialgebroid" (as in the linked nlab page). In more recent literatur …

I will jot down some stray (and easy) thoughts, in an effort to engage the question and see whether some aspects of it can be made more precise. Going out on a limb, I suppose a baseline assumption …

Comment by Cherng-tiao Perng converted to an answer: It appears that Theorem A of this paper solves your problem.

It's not very clear to me what the actual question is. If you know how to compute successive decimal approximations to a number like $\sqrt[3]{5}$, then surely you know how to compute its continued fr …

As requested, I'll turn my comments into an answer. There were two questions, the first being what we call the representing object if a presheaf $c \mapsto \mathcal{D}(F c, d)$ is representable, and t …

In general $F$ preserves neither pullbacks nor even products. In a comment I mentioned that the "discrete graph" functor $\text{Set} \to \text{Set}^{\bullet \rightrightarrows \bullet}$ is full and fai …

Note: Fedor and Vladimir have already answered the question, but this is a partial answer in the other direction, under a stronger hypothesis. (This answer, which I had earlier deleted, has been edite …

Connes was a member, according to M. Mashaal "Bourbaki: A secret society of mathematicians", AMS 2006 (translated from the French by A. Pierrehumbert). It says so on page 18; see the link. But, as wa …

Another categorical example: the laws of arithmetic, as applied to the arithmetic of finite integers, are ultimately explicable by the fact that the category of finite sets $\mathbf{Fin}$ is a cartesi …

(This answer is Community Wiki and is extracted from comments by user eric, who has declined to post them as an answer. The CW is to invite others to contribute, especially to provide suitable referen …

Four ants are on the corners of a square, each facing its neighbor in the counterclockwise direction. At the same time each begins marching towards its neighbor, all at the same speed. After moving th …