MathOverflow

I would like to understand filtered colimits in finite categories a bit better. In my recent question MO/509853 Simon Henry has shown that every finite Cauchy complete category has filtered colimits (and in fact, is finitely accessible). But the proof...

I have been looking at some finite categories recently and noticed that many of them have a generator and a cogenerator. In fact, in CatDat, currently every finite inhabited category has a generator and a cogenerator (search result), and this has been...

The self-similar solution of Navier-Stokes has the form as follows (the $u=(t-T)^{\lambda}U(y)$) has only form of $\lambda = -1/2$.
The work of V. SVERAK et. al. above shows that if $U\in H^1(R^3)$ or more general $U\in L^3(R^3)$ the only solution is $U=0$. Do we need to make effort to seek the solution $U$ which doesn't belong to $L^3(R^3)$ (and so doesn't belong to $H^1(R^3)$?...

Let $n\in\mathbb{N}$ such that $n\geq 2$ and let $0<r<1$ be a real number. We wish to solve the following problem.
$$\min_{(t,(z_j)_{j=2}^n) \in \mathbb{R}\times \mathbb{Z}^{n-1}} t$$
subject to :