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1d
comment “Nice proof” that the unit of the left Kan extension of $F$ is an isomorphism, if $F$ is fully faithful
If the left adjoint is fully faithful then the unit is an isomorphism.
2d
revised Are there any theorems about functors that reflect exactness?
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Jan
26
asked Are there any theorems about functors that reflect exactness?
Jan
26
revised Is my observation correct regarding restriction of scalars?
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Jan
26
accepted Presheaf image of a monomorphism of sheaves is a sheaf
Jan
26
asked Is my observation correct regarding restriction of scalars?
Jan
25
revised Image sheaf is the sheafification of the image presheaf
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Jan
25
comment Image sheaf is the sheafification of the image presheaf
Yes, in the sense that the natural map between them is an isomorphism. This holds in any abelian category, and in fact characterizes abelian categories (from additive categories).
Jan
25
comment Presheaf image of a monomorphism of sheaves is a sheaf
You are right, I was always thinking about image and naively just reduced to cokernel. What about current version regarding image?
Jan
25
revised Presheaf image of a monomorphism of sheaves is a sheaf
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Jan
25
accepted Colimit preserves monomorphisms under certain conditions
Jan
25
revised Colimit preserves monomorphisms under certain conditions
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Jan
25
comment Colimit preserves monomorphisms under certain conditions
@tracing It is $f: \varinjlim A_i\to \varinjlim B_i$ induced by $f_i:A_i\to B_i$
Jan
25
revised Image sheaf is the sheafification of the image presheaf
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Jan
25
asked Presheaf image of a monomorphism of sheaves is a sheaf
Jan
24
revised Image sheaf is the sheafification of the image presheaf
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Jan
24
asked Image sheaf is the sheafification of the image presheaf
Jan
23
awarded  Popular Question
Jan
23
awarded  Yearling
Jan
23
comment Colimit preserves monomorphisms under certain conditions
@Krish That's true, but I'm in particular interested in $\mathbf{Set}$.