2024-06-03

607: Congruence on Category

<The previous article in this series | The table of contents of this series | The next article in this series>
definition of congruence on category

Topics


About: category

The table of contents of this article

Starting Context

Target Context


  • The reader will have a definition of congruence on category.

Orientation


There is a list of definitions discussed so far in this site.

There is a list of propositions discussed so far in this site.

Main Body

1: Structured Description


Here is the rules of Structured Description.

Entities:
C: ∈{ the categories }
∗∼: ∈{ the equivalence relations on Mor(C)}
//

Conditions:
f1∼f2⟹∃O1,O2∈Obj(C)(f1,f2∈Mor(O1,O2))
∧
∀O1,O2,O3∈Obj(C)(∀f1,f2∈Mor(O1,O2),∀f3,f4∈Mor(O2,O3)((f1∼f2∧f3∼f4)⟹(f3∘f1∼f4∘f2)))
//

2: Natural Language Description


For any category, C, any equivalence relation on Mor(C), ∼, such that f1∼f2⟹∃O1,O2∈Obj(C)(f1,f2∈Mor(O1,O2)) and ∀O1,O2,O3∈Obj(C)(∀f1,f2∈Mor(O1,O2),∀f3,f4∈Mor(O2,O3)((f1∼f2∧f3∼f4)⟹(f3∘f1∼f4∘f2)))

References
<The previous article in this series | The table of contents of this series | The next article in this series>
Posted by at
Labels: