# Differences

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schroeder_categories [2010/07/29 15:46]
127.0.0.1 external edit
schroeder_categories [2016/11/28 19:04] (current)
jipsen
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-=====Name of class===== +=====Schroeder categories=====
-% Note: replace "Template" with Name_of_class in previous line+
-Abbreviation: **Abbr**+Abbreviation: **SchrCat**
====Definition==== ====Definition====
-A \emph{...} is a structure $\mathbf{A}=\langle A,...\rangle$ of type $\langle +A \emph{Schroeder category} is an enriched [[category]]$\mathbf{C}=\langle C,\circ,\text{dom},\text{cod}\rangle$-...\rangle$ such that+
-$\langle A,...\rangle$ is a [[name of class]] +in which every hom-set is a Boolean algebras.
- +
-$op_1$ is (name of property):  $axiom_1$ +
- +
-$op_2$ is ...:  $...$ +
- +
-Remark: This is a template. +
- +
-It is not unusual to give several (equivalent) definitions. Ideally, one of the definitions would give an irredundant axiomatization that does not refer to other classes.+
==Morphisms== ==Morphisms==
-Let $\mathbf{A}$ and $\mathbf{B}$ be ... . A morphism from $\mathbf{A}$ to $\mathbf{B}$ is a function $h:A\rightarrow B$ that is a homomorphism:  +Let $\mathbf{C}$ and $\mathbf{D}$ be Schroeder categories. A morphism from $\mathbf{C}$ to $\mathbf{D}$ is a function $h:C\rightarrow D$ that is a \emph{functor}: $h(x\circ y)=h(x)\circ h(y)$, $h(\text{dom}(x))=\text{dom}(h(x))$ and $h(\text{cod}(x))=\text{cod}(h(x))$.
-$h(x ... y)=h(x) ... h(y)$ +
- +
-====Definition==== +
-An \emph{...} is a structure $\mathbf{A}=\langle A,...\rangle$ of type $\langle + -...\rangle$ such that+
-$...$ is ...: $axiom$ +Remark: These categories are also called \emph{groupoids}.
-   +
-$...$ is ...:  $axiom$+
====Examples==== ====Examples====
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Feel free to add or delete properties from this list. The list below may contain properties that are not relevant to the class that is being described. Feel free to add or delete properties from this list. The list below may contain properties that are not relevant to the class that is being described.
-^[[Classtype]]                        |(value, see description) [(Ln19xx)]  |+^[[Classtype]]                        |first-order class |
^[[Equational theory]]                | | ^[[Equational theory]]                | |
^[[Quasiequational theory]]           | | ^[[Quasiequational theory]]           | |
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f(4)= &\\   f(4)= &\\
f(5)= &\\   f(5)= &\\
-\end{array}$-$\begin{array}{lr}
f(6)= &\\   f(6)= &\\
f(7)= &\\   f(7)= &\\
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f(10)= &\\   f(10)= &\\
\end{array}$\end{array}$
+
====Subclasses==== ====Subclasses====
-  [[...]] subvariety +[[...]]
- +
-  [[...]] expansion +
====Superclasses==== ====Superclasses====
-  [[...]] supervariety +[[Categories]]
- +
-  [[...]] subreduct +
====References==== ====References====