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Dec
6
asked Category defined by a finite commutative diagram
Dec
5
comment Why “thin groupoids” are not ubiquitous?
Oh, I see: Some people use the word "setoid" differently. So my downvote was a mistake. I can't upvote it back now, sorry.
Dec
5
comment Why “thin groupoids” are not ubiquitous?
This your definition of setoids is not equivalent (however, it is equivalent up to equivalence of categories) to the standard definition of setoids, that is a set with an equivalence relation. Equivalence up to equivalence of categories is not enough for my purposes. I still think that I downvoted correctly,
Dec
5
comment Why “thin groupoids” are not ubiquitous?
Setoid is a set with an equivalence relation on it. (And I know it long ago before I've read your answer.) I understand this. I downvote because switching from a groupoid to a setoid leads to information loss, and this makes it not an answer to my question.
Dec
5
comment Why “thin groupoids” are not ubiquitous?
I need to describe a category. A category contains not only objects but also morphisms. As my category happens to be thin, there is a (not necessarily entire defined) function from pairs of objects into a morphism. Having a setoid we cannot define such a function. But I need this function. I need to be able to get the morphisms whenever a pair of objects is specified. Having only a setoid, I cannot do this.
Dec
5
comment Why “thin groupoids” are not ubiquitous?
But having two elements of setoids, I cannot restore particular morphism (such as $f\mapsto f\cap\Gamma$). It is not what I need
Dec
5
comment Why “thin groupoids” are not ubiquitous?
I yet don't understand you and don't see how to express this with setoids. When we switch from a thin groupoid to a setoid, the information about particular morphisms is lost (they are just replaced with a pair of objects), but the whole thing I need is information about what are particular morphisms, depicted as arrows in my diagrams.
Dec
5
comment Why “thin groupoids” are not ubiquitous?
I don't get how this is related with setoids. How to express my diagrams using setoids? I need particular isomorphisms not just the fact that two objects are isomorphic.
Dec
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revised Why “thin groupoids” are not ubiquitous?
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asked Why “thin groupoids” are not ubiquitous?
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comment Another way to express certain filter
See also counter-examples in this thread: groups.google.com/forum/#!topic/sci.math/Plru0S8ePzs
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