# Differences

This shows you the differences between two versions of the page.

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. | + | |

- | If you know something about this class, click on the 'Edit text of this page' link at the bottom and fill out this page. | + | |

- | | + | |

- | 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==== |

Trace: