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September 16, 2013 / porton

New concept: metamonovalued morphisms

Let fix some dagger category every of Hom-sets of which is a complete lattice, and the dagger functor agrees with the lattice order.

I define a morphism f to be monovalued when \circ f^{-1}\le \mathrm{id}_{\mathrm{Dst}\, f}.

I call a morphism f metamonovalued when (\bigwedge G) \circ f = \bigwedge_{g \in G} ( g \circ f) for every set G of morphims (provided that the sources and domains of the morphisms are suitable). Here \bigwedge denoted the infimum on the above mentioned complete lattice.

In my book (recently added to the preprint) I have proved that every monovalued funcoid is metamonovalued. Thus there is probably some connection between monovalued and metamonovalued morphisms.

The following problems are yet open:

Question Is every metamonovalued funcoid monovalued?

Question Is every metamonovalued reloid monovalued?

Question Is every monovalued reloid metamonovalued?

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