query: How to construct a natural isomorphism of hom-sets from an adjunction of functors
positive_passages.docid: 156178
positive_passages.text: Do counit-unit adjunctions have the expected universal properties?
negative_passages.docid: 52354
negative_passages.text: Given a idempotent endomorphism, show that $M = \ker(f) \oplus \ker (f-\text{id}_M)$
negative_passages.docid: 126644
negative_passages.text: Simple module and homomorphisms
negative_passages.docid: 145722
negative_passages.text: Prove there is a bijection between the set of $R[x]$-module structures on $M$ and $\mathrm{End}_{R-\mathsf{Mod}}(M)$.
negative_passages.docid: 55778
negative_passages.text: Group theoretic meaning of natural isomorphisms between certain functors
negative_passages.docid: 38691
negative_passages.text: Injectivity of Homomorphism in Localization
negative_passages.docid: 134458
negative_passages.text: Isomorphisms preserving integral domains and fields
negative_passages.docid: 70658
negative_passages.text: Isomorphism between quotient modules
negative_passages.docid: 135422
negative_passages.text: $\operatorname{Hom}(-,A) \cong \operatorname{Hom}(-,A') \Rightarrow A \cong A'$, proof verification
negative_passages.docid: 137907
negative_passages.text: Composing functors with natural transformations
negative_passages.docid: 28518
negative_passages.text: Hom of finitely generated modules over a noetherian ring
negative_passages.docid: 77757
negative_passages.text: Infer the second isomorphism theorem from the first one
negative_passages.docid: 23279
negative_passages.text: Group Theory Isomorphism
negative_passages.docid: 128266
negative_passages.text: Dual Spaces and Natural maps
negative_passages.docid: 143648
negative_passages.text: Reconciling different definitions of left-exact functor
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: 121246
negative_passages.text: Projective modules and $\hom(P,\cdot)$