query: How to prove snake lemma in abelian categories without invoking Mitchell's embedding theorem?
positive_passages.docid: 25064
positive_passages.text: Proving the snake lemma without a diagram chase
negative_passages.docid: 123130
negative_passages.text: Showing an isomorphism between exterior products of a free module
negative_passages.docid: 6904
negative_passages.text: questions about extremal epimorphisms in category theory
negative_passages.docid: 60674
negative_passages.text: Finitely generated idempotent ideals are principal: proof without using Nakayama's lemma
negative_passages.docid: 106927
negative_passages.text: How do I prove $[G:H\cap K]\leq [G:H][G:K]$?
negative_passages.docid: 115782
negative_passages.text: Proof $\mathbb{A}^n$ is irreducible, without Nullstellensatz
negative_passages.docid: 53335
negative_passages.text: Why isn't $\mathbb{C}[x,y,z]/(xz-y)$ a flat $\mathbb{C}[x,y]$-module
negative_passages.docid: 122012
negative_passages.text: The ideal $(x,y)$ is not a free $K[x,y]$-module
negative_passages.docid: 108955
negative_passages.text: Showing $(\mathbb{Q},+)$ is not isomorphic to $(\mathbb{R},+)$
negative_passages.docid: 5599
negative_passages.text: Proving an inclusion for the derived group
negative_passages.docid: 101064
negative_passages.text: Showing the triviality of homomorphisms
negative_passages.docid: 47630
negative_passages.text: Endomorphisms of modules satisfying chain conditions and counterexamples.
negative_passages.docid: 100134
negative_passages.text: Proving existence of a surjection $2^{\aleph_0} \to \aleph_1$ without AC
negative_passages.docid: 94246
negative_passages.text: Category-theoretic limit related to topological limit?
negative_passages.docid: 125894
negative_passages.text: Prove that $\mathbb{Q}$ belongs to the Borel $\sigma$-algebra of $\mathbb{R}$
negative_passages.docid: 78211
negative_passages.text: Equivalence of categories preserves cartesian closedness
negative_passages.docid: 76501
negative_passages.text: How can we show that $\mathbb Q$ is not a free $\mathbb Z$-module?