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This is one of the proofs currently on the nLab. My goal in writing it was to see how elementary I could make it, that if you squint a little it might have been a proof from the late $18^{th}$ century …

First, an answer to Pete Clark's comment on the Chinese remainder theorem can be found in Floris Ernst's 2004 University of Otago Master's thesis Multiplicative ideal theory (pdf link). Prüfer domains …

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 $\ …

According to unpublished notes by Gavin Wraith ("Notes on arithmetic universes and Gödel incompleteness theorems" (1985)), PRA can be described as an equational theory or as a Lawvere theory, and is a …

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 …

Why not look at Stasheff's original paper? He does give a point-set model (where $K_{n+2}$ is a compact convex semialgebraic subset of $\mathbb{R}^n$) and describes explicitly the substitution maps $\ …

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 …