Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

There is a functor $\mathit{Iso} : \mathbf{Cat} \rightarrow \mathbf{Cat}$ which identifies the subcategory of a category in which only the isomorphisms appear as arrows — i.e. it strips off any arrow that does not have an inverse. This is because identities are isomorphisms, a composition of isomorphisms is an isomorphism, and functors preserve isomorphism.

My question is this: can this functor be constructed out of more familiar categorical concepts? For example, is it a limit of some diagram in $\mathbf{Cat}$? Also, is there a standard name for this functor?

share|improve this question
    
Presumably, this is just curiosity, so you have not seen it in nature yourself right? –  Karl Kronenfeld Mar 28 '13 at 2:11
    
@user67848, In nature? I have seen it often (wearing another mask) when I am writing Haskell code. –  luqui Mar 28 '13 at 3:32
add comment

1 Answer 1

up vote 5 down vote accepted

This functor really takes values in the category of (small) groupoids $\text{Gpd}$. Once you've made that modification, it's the right adjoint to the inclusion functor $\text{Gpd} \to \text{Cat}$, which exhibits $\text{Gpd}$ as a coreflective subcategory of $\text{Cat}$. It is sometimes called the core.

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.