[[!redirects tabular dagger 2-posets]] [[!redirects tabulation]] ## Contents ## * table of contents {:toc} ## Idea ## A dagger 2-poset with tabulations, such as a tabular allegory. ## Definition ## A **tabular dagger 2-poset** is a [[dagger 2-poset]] $C$ such that for every object $A:Ob(C)$ and $B:Ob(C)$ and morphism $R:Hom(A,B)$, there is an object $\vert R \vert:Ob(C)$ and [[map in a dagger 2-poset|maps]] $f:Hom(\vert R \vert, A)$, $g:Hom(\vert R \vert, B)$, such that $R = f^\dagger \circ g$ and for every object $E:Ob(C)$ and maps $h:Hom(E,\vert R \vert)$ and $k:Hom(E,\vert R \vert)$, $f \circ h = f \circ k$ and $g \circ h = g \circ k$ imply $h = k$. ## Properties ## The [[category of maps]] of a tabular dagger 2-poset has all [[pullback]]s. ## Examples ## The dagger 2-poset of sets and relations is a tabular dagger 2-poset. ## See also ## * [[dagger 2-poset]]