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schroeder_categories [2016/11/27 10:18]
jipsen
schroeder_categories [2016/11/28 19:04] (current)
jipsen
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====Definition==== ====Definition====
-A \emph{Schroeder category} is a [[category]] $\mathbf{C}=\langle C,\circ,\text{dom},\text{cod}\rangle$ such that+A \emph{Schroeder category} is an enriched [[category]] $\mathbf{C}=\langle C,\circ,\text{dom},\text{cod}\rangle$
-every morphism is an isomorphism: $\forall x\exists y\ x\circ y=\text{dom}(x)\text{ and }y\circ x=\text{cod}(x)$ +in which every hom-set is a Boolean algebras.
==Morphisms== ==Morphisms==
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$\begin{array}{lr} $\begin{array}{lr}
  f(1)= &1\\   f(1)= &1\\
-  f(2)= &1\\ +  f(2)= &\\ 
-  f(3)= &2\\ +  f(3)= &\\ 
-  f(4)= &3\\ +  f(4)= &\\ 
-  f(5)= &7\\ +  f(5)= &\\ 
-  f(6)= &9\\ +  f(6)= &\\ 
-  f(7)= &16\\ +  f(7)= &\\ 
-  f(8)= &22\\ +  f(8)= &\\ 
-  f(9)= &42\\ +  f(9)= &\\ 
-  f(10)= &57\\+  f(10)= &\\
\end{array}$ \end{array}$
-http://oeis.org/A140189+
====Subclasses==== ====Subclasses====
-[[Groups]]+[[...]]
====Superclasses==== ====Superclasses====