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Let $C$ be a category with finite limits; that is, for any finite category $D$ and functor $F:D\to C$ the category $\mathrm{Cone} F$ of cones over $F$ is inhabited and has terminal objects (we could t …

I notice that the categories considered for naming here are all the domains, or shapes, of basic diagrams; an object, an arrow, an endomorphism (n.b., my instinct was just to call that $\mathbb{N}$), …

So, in $R-Mod$, we have the rather short sequence $\mathrm{Ext}^0(A,B)\cong Hom_R(A,B) $ $\mathrm{Ext}^1(A,B)\cong \mathrm{ShortExact}(A,B)\mod \equiv $, equivalence classes of "good" factorization …

Do people tend to mean the official definition? I think "official" belongs in scare-quotes... I tend to think that "subcategory" is an evil notion. I'm not published anywhere, but in my notes …

An incomplete answer on the subject of countable dense linear orders without endpoints; I left some other thoughts at the Cafe; on further reflection, one can think of the maps $\cdot\times \frac{p}{ …

As it happens, the klein hyperbolic models, the usual euclidean plane, and central projection for projective space all have geodesics that look like straight lines; on the other hand, these maps can't …

First, it's important that the infinite connect sum $A\# B\#A\#\cdots$ is not the limit of the finite connect sums $A,A\#B, A\#B\# A,\dots$; in fact, I'm sure the binary connect sum is as wrong a nota …

I'm betting on Supremum.

I'd just like to point out that there is a monad on $Top$, (which in the homotopy category looks rather dull,) assigning to each space $X$ its cone $CX$, the mapping cylinder of $X\to * $. The unit m …

There are a short list of operations described as generating the desired polyhedra: $ X : \mathrm{Prism} \vdash C X : \mathrm{Prism} $ $ l : \mathrm{list}\ \mathrm{Prism} \vdash \Pi l : \mathrm{ …

I have two related sorts of example to suggest, probably exhibiting my categorical bias vs. the analytic/geometric-topology weight of the preceding examples. Galois-theoretic Let $P\in K[x]$ be an i …