query: When is the image of a Functor a category
positive_passages.docid: 80260
positive_passages.text: Can it happen that the image of a functor is not a category?
negative_passages.docid: 122110
negative_passages.text: Character of the subobject classifier in the topos of $\mathbf{M}$-sets.
negative_passages.docid: 140314
negative_passages.text: A module as an external direct product of the kernel and image of an idempotent function
negative_passages.docid: 44396
negative_passages.text: Noetherian Ring under a Homomorphism / homomorphic function / map
negative_passages.docid: 90192
negative_passages.text: Kernel and Image of a group homomorphism
negative_passages.docid: 110059
negative_passages.text: $A^A$ in category of graphs
negative_passages.docid: 126472
negative_passages.text: Surjective endomorphisms of uniserial modules
negative_passages.docid: 7441
negative_passages.text: Hom is a left-exact functor
negative_passages.docid: 40678
negative_passages.text: Image of an ideal under a surjective ring homomorphism is an ideal
negative_passages.docid: 73513
negative_passages.text: UMP of product functor
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: 106306
negative_passages.text: $X^*$ with its weak*-topology is of the first category in itself
negative_passages.docid: 51245
negative_passages.text: $A \longrightarrow \text{Im} f$ is an epimorphism and a cokernel of ker $f \longrightarrow A$ in every abelian category
negative_passages.docid: 87203
negative_passages.text: Preimage of generated $\sigma$-algebra
negative_passages.docid: 67237
negative_passages.text: Pull back image of maximal ideal under surjective ring homomorphism is maximal
negative_passages.docid: 52554
negative_passages.text: Showing that localization is an exact functor
negative_passages.docid: 28154
negative_passages.text: Riehl's Category Theory in Context - Exercise 2.1.iv.