MathOverflow

A reflexive coequalizer is a special type of coequalizer which often exists even when general coequalizers might not exist. I wonder if the category of smooth manifolds $\mathbf{Man}$ has reflexive coequalizers, and likewise, coreflexive equalizers.
Both coequalizers and equalizers do not exist in general (MO/19116 and MSE/322485). I might be wrong, but I think the counterexamples do not work here. It is worth mentioning that $\mathbf{Man}$ is Cauchy complete (Thm. 2.1 in nLab), which is yet another...

I have realized that the walking parallel pair category $\{0\rightrightarrows 1\}$ has all sifted colimits.I noticed this while working on an attempt to fill in the missing data in CatDat, a recently opened category theory database.My proof can be found...

Assume that someone placed a bunch of dominos on an $n \times n$ grid.
We say that a path is domino-respecting if whenever it contains one half of a domino, that half is connected to the other half of the domino in the path.
(This is kind of like a pairing strategy in combinatorial game theory.)...

Let $A$ be an N-function and suppose that$$\int^{+\infty}_1\frac{A^{-1}(\tau)}{\tau^{1+\frac{1}{n}}}d\tau=+\infty. $$We denote by $\widehat{A}$ an N-function equal to $A$ near infinity and $\widehat{A}$ satisfies
$$\int^{1}_0\frac{\widehat{A}^{-1}(\tau)}{\tau^{1+\frac{1}{n}}}d\tau<+\infty. $$...