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 Dec6 asked Category defined by a finite commutative diagram Dec5 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. Dec5 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, Dec5 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. Dec5 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. Dec5 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 Dec5 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. Dec5 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. Dec5 revised Why “thin groupoids” are not ubiquitous? added 156 characters in body Dec5 asked Why “thin groupoids” are not ubiquitous? Dec2 comment Another way to express certain filter See also counter-examples in this thread: groups.google.com/forum/#!topic/sci.math/Plru0S8ePzs Dec1 revised Another way to express certain filter added 221 characters in body Dec1 revised Another way to express certain filter [Edit removed during grace period] Dec1 revised Another way to express certain filter deleted 8 characters in body Dec1 answered Another way to express certain filter Dec1 revised Another way to express certain filter edited body Dec1 revised Another way to express certain filter added 39 characters in body Dec1 revised Another way to express certain filter added 3 characters in body Dec1 revised Another way to express certain filter added 240 characters in body Dec1 revised Another way to express certain filter added 179 characters in body