Problem 5. Let Cat be the category of small categories. Let 1 be the category with a single object • and only the identi

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Problem 5. Let Cat be the category of small categories. Let 1 be the category with a single object • and only the identi

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Problem 5 Let Cat Be The Category Of Small Categories Let 1 Be The Category With A Single Object And Only The Identi 1
Problem 5 Let Cat Be The Category Of Small Categories Let 1 Be The Category With A Single Object And Only The Identi 1 (44.89 KiB) Viewed 28 times
Problem 5. Let Cat be the category of small categories. Let 1 be the category with a single object • and only the identity arrow. Let 2 be the category with two objects, {0,1}, which besides the identity arrows has a single arrow 1 + 2. Define functors Arr: Cat + Set and Obj: Cat → Set (obvious from their names but do provide details). Give a representation for these functors. The functor 0:1 + 2 maps the object • to the object ( in 2. It will define a natural transformation between the corresponding representable functors what is it?
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