query: Examples of canonical projections that are not epimorphisms and canonical injections that are not
positive_passages.docid: 141732
positive_passages.text: Are all projection maps in a categorical product epic?
negative_passages.docid: 93358
negative_passages.text: Find an example of a non-surjective field endomorphism
negative_passages.docid: 146812
negative_passages.text: Explicit construction for unitary extensions of completely positive and trace preserving (CPTP) maps?
negative_passages.docid: 54333
negative_passages.text: In categorical terms, why is there no canonical isomorphism from a finite dimensional vector space to its dual?
negative_passages.docid: 90826
negative_passages.text: Constructing a subset not in $\mathcal{B}(\mathbb{R})$ explicitly
negative_passages.docid: 116112
negative_passages.text: Examples of 'almost' vector spaces where unitary law fails
negative_passages.docid: 103924
negative_passages.text: Kernel of a substitution map
negative_passages.docid: 143869
negative_passages.text: Showing that the norm of the canonical projection $X\to X/M$ is $1$
negative_passages.docid: 108567
negative_passages.text: Nielsen & Chuang Exercise 2.2 - “Matrix representations: example”
negative_passages.docid: 145462
negative_passages.text: On the canonical isomorphism between $V$ and $V^{**}$
negative_passages.docid: 113863
negative_passages.text: The non-existence of non-principal ultrafilters in ZF
negative_passages.docid: 32127
negative_passages.text: Example where $f\circ g$ is bijective, but neither $f$ nor $g$ is bijective
negative_passages.docid: 136592
negative_passages.text: Examples of manifolds that are not boundaries
negative_passages.docid: 10715
negative_passages.text: Orthogonal projection and two subspaces
negative_passages.docid: 101095
negative_passages.text: Constructing an example s.t. $\operatorname{Hom}_R(M,N)$ is not finitely generated
negative_passages.docid: 127025
negative_passages.text: Diagonalization of a projection
negative_passages.docid: 24828
negative_passages.text: surjective immersion $\mathbb{R}^2 \to \mathbb{R}^2$ which is not a diffeomorphism