![](/files/happy5.png)
Conjecture
for every filter objects
,
.
![$ \left( \mathcal{A} \ltimes \mathcal{B} \right) \cup \left( \mathcal{A} \rtimes \mathcal{B} \right) = \mathcal{A} \times^{\mathsf{\ensuremath{\operatorname{RLD}}}} \mathcal{B} $](/files/tex/985106da22b932d63d15946e484e9de0ba9c261d.png)
![$ \mathcal{A} $](/files/tex/3abde4ab7e21fe6fad91d0a03ad306c2c82659d9.png)
![$ \mathcal{B} $](/files/tex/cca7b496bd14e6acf10041305acbd75cd720f9b3.png)
See Algebraic General Topology for definitions of used concepts.
I proved it false based on a solution of an equivalent elementary problem by Andreas Blass.
Bibliography
*Victor Porton. Algebraic General Topology
* indicates original appearance(s) of problem.