I updated my online draft of the “Filters on Posets and Generalizations” article, while a former version of it was submitted as a preprint into Armenian Journal of Mathematics.

The main new feature of my online draft is the section “Complementive filter objects and factoring by a filter” added and also a counterexample against this conjecture.

The isomorphism of complementive filters and factoring by a filter and the counter-example were suggested by Andreas Blass in his answer to this my MathOverflow question.