# Tagged Questions

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### Defining Test-Objects

In various categories one encounters what are referred to as 'test-objects'. For example, singleton set serves as test-object (in testing the equality of functions) in the category of sets. In the ...
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### Allegories in easy words?

1) What is, in easy words, the definiton of an allegory? 2) And when are allegories useful? What does it have to do with the category theory and categories? With the definiton of category, ...
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### In a groupoid, do any two objects have a morphism between them?

This is a question about the definition of a groupoid (in category theory). I've read the Wikipedia article, and it says that a groupoid is a small category in which every morphism is an isomorphism. ...
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### Are bicategories and lax 2-categories the same?

My question is that whether the definition of bicategories is the same as the definition of lax 2-categories. I heard that they are both week versions of 2-categories. Are they the same? If not, how ...
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### Are distinctions in definitions of “finite” material in, eg, topology or measure theory?

There are several definitions of "finite", like Dedekind's and Tarski's (Thanks to A.K. for point out the latter - first time I've heard of it): From the Wikipedia entry on Finite Set: (Richard ...
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### Name for the initial object of a connected component of a category

I was just wondering whether there is already a name for an object of a category as described below. Recall that an initial object in a category $\mathcal C$ is an object $I\in\mathcal C$ such that ...
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### Question about the definition of a category

I am confused about the definition of a category given in the Wikipedia article on Category theory: It seems to me that the structure being described (the "arrows" between objects in some class) is ...
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### Definition of a groupoid of fractions

The title sums it up : I am looking for a definition of "a groupoid of fractions for a category". I would be interested in any example someone might have as well...