query: Showing when two functors are naturally isomorphic, if one is faithful, then the other also is.
positive_passages.docid: 140503
positive_passages.text: What properties do natural isomorphisms between functors preserve?
negative_passages.docid: 23579
negative_passages.text: If $G$ is isomorphic to $H$, then ${\rm Aut}(G)$ is isomorphic to ${\rm Aut}(H)$
negative_passages.docid: 20030
negative_passages.text: Is an equivalence an adjunction?
negative_passages.docid: 37041
negative_passages.text: Why is $\text{Aut}(F)$ of the forgetful functor $F$ on $G$-sets isomorphic to $G$?
negative_passages.docid: 98992
negative_passages.text: A morphism of sheaves of sets is an isomorphism if it induces an isomorphism of all stalks.
negative_passages.docid: 125982
negative_passages.text: If the dual spaces are isometrically isomorphic are the spaces isomorphic?
negative_passages.docid: 89190
negative_passages.text: Why is it true that $|AB:A|=|B:A\cap B|$ even if $A$ is not normal in $AB$? (Second Isomorphism Theorem)
negative_passages.docid: 123130
negative_passages.text: Showing an isomorphism between exterior products of a free module
negative_passages.docid: 108156
negative_passages.text: Algebraic closure of $\mathbb{C}(x)$ is isomorphic to $\mathbb{C}$
negative_passages.docid: 52554
negative_passages.text: Showing that localization is an exact functor
negative_passages.docid: 124003
negative_passages.text: Composition of adjoint functors
negative_passages.docid: 3778
negative_passages.text: If the matrix rings over two Rings of the same size are isomorphic, then the scalar rings are isomorphic
negative_passages.docid: 121465
negative_passages.text: $R[x]$ has a subring isomorphic to $R$.
negative_passages.docid: 70872
negative_passages.text: Isomorphism of quotient modules implies isomorphism of submodules?
negative_passages.docid: 114916
negative_passages.text: $\mathbb Z_{mn}$ isomorphic to $\mathbb Z_m\times\mathbb Z_n$ whenever $m$ and $n$ are coprime
negative_passages.docid: 8587
negative_passages.text: What is an example of two k-algebras that are isomorphic as rings, but not as k-algebras?
negative_passages.docid: 53531
negative_passages.text: Birational and faithfully flat $\implies$ isomorphism