query: If $f$ is injective and $g$ is not injective, $g\circ f$ is not injective?
positive_passages.docid: 89514
positive_passages.text: Show that if $g \circ f$ is injective, then so is $f$.
negative_passages.docid: 101042
negative_passages.text: Suppose we have functions $f:A→B$ and $g:B→C$. Prove that if $f$ and $g$ are invertible, then so is $g \circ f$.
negative_passages.docid: 151047
negative_passages.text: a non trivial example: $G/H$ is isomorphic to $G$
negative_passages.docid: 148616
negative_passages.text: When is a ring homomorphism $A \to A$ surjective but not injective.
negative_passages.docid: 106809
negative_passages.text: $f: G→G$ defined by $f(x) =x^2$ is a homomorphism if and only if $G$ is abelian.
negative_passages.docid: 72644
negative_passages.text: Continuous injective map $f:\mathbb{R}^3 \to \mathbb{R}$?
negative_passages.docid: 25050
negative_passages.text: To prove that $(F,+)$ and $(F-\{0\},\cdot)$ are not isomorphic as groups.
negative_passages.docid: 65977
negative_passages.text: Showing function is injective iff $f(M_1 \cap M_2) = f(M_1)\cap f(M_2)$
negative_passages.docid: 105455
negative_passages.text: Prove that "injective function $f:X\to Y$ exists" and "surjective function $g:Y\to X$ exists" is logically equivalent.
negative_passages.docid: 88645
negative_passages.text: Prove that the additive groups $\mathbb{R}$ and $\mathbb{Q}$ are not isomorphic.
negative_passages.docid: 82046
negative_passages.text: prove that this double transpose $T''$ it's not injective.
negative_passages.docid: 152438
negative_passages.text: Is the composition of two injective functions injective?
negative_passages.docid: 45710
negative_passages.text: Finishing a proof: $f$ is injective if and only if it has a left inverse
negative_passages.docid: 157378
negative_passages.text: On an injective ring homomorphism from the ring of continuous functions to the ring of differentiable functions
negative_passages.docid: 111689
negative_passages.text: Surjective, but not injective endomorphism
negative_passages.docid: 12455
negative_passages.text: $|G|>2$ implies $G$ has non trivial automorphism
negative_passages.docid: 22758
negative_passages.text: If $\operatorname{ran} F \subseteq \operatorname{dom} G$, then $\operatorname{dom}(G \circ F) = \operatorname{dom} F$.