[[!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 exist an object $\vert R \vert$ called a **tabulation** of $R$ and [[map in a dagger 2-poset|maps]] $f:Hom(\vert R \vert, A)$ and $g:Hom(\vert R \vert, B)$ such that $R = g \circ f^\dagger$, and for every object $E:Ob(C)$ and maps $h:Hom(E,A)$ and $k:Hom(E,B)$, $k \circ h^\dagger \leq R$ if and only if there exists a unique map $j:E \to \vert R \vert$ such that $h = f \circ j$ and $k = g \circ j$. ## Examples ## The dagger 2-poset of sets and relations is a tabular dagger 2-poset. ## See also ## * [[dagger 2-poset]] * [[cartesian dagger 2-poset]]