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Mar
21
awarded  Famous Question
Mar
21
answered When are canonical maps between limits monomorphisms?
Mar
21
awarded  Nice Answer
Mar
19
awarded  Notable Question
Mar
19
awarded  Nice Answer
Mar
18
comment Smooth completion of algebraic curves
Yes, that's one way of doing it. Blowups are birational and every birational equivalence class of projective algebraic curves contains a unique smooth algebraic curve.
Mar
18
comment Smooth completion of algebraic curves
Even in that case it can happen that the projective closure is not smooth.
Mar
18
comment Smooth completion of algebraic curves
Given a smooth (affine) algebraic curve embedded in some affine space, its projective closure can fail to be smooth. The correct procedure is described in §6 of [Hartshorne, Ch. I].
Mar
17
comment Can some Lie groups ($S^3$ in particular) be converted to simplicial groups?
The singular simplicial set functor takes topological groups to simplicial groups.
Mar
16
revised Intuitionistic logic unit type as truth
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Mar
14
comment Defining Presheaves on Categories
Actually, you don't need to assume the existence of limits. The sheaf condition can be restated in the form "<a certain cone> is a limiting cone".
Mar
14
revised Defining Presheaves on Categories
deleted 18 characters in body
Mar
14
comment Defining adjoint functors: What does “natural bijection” mean?
The second sentence is just repeating what the first sentence is saying in more basic terms. If you unfold the definition of natural isomorphism you will see this.
Mar
14
comment $(R^{\oplus A})^{\oplus B} \approx R^{\oplus (A\times B)}$?
You need to use the fact that, for sets, multiplication really is just repeated addition.
Mar
14
awarded  Popular Question
Mar
14
comment Square is homotopy Cartesian if horizontal maps are weak equivalences
It's actually true in any model category (or even any category with weak equivalences) but the proof would be different.
Mar
13
revised Necessity of Category Theory for understanding Algebraic Topology
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Mar
13
answered Good textbooks on homological algebra
Mar
12
awarded  Revival
Mar
10
answered Morphism epimorphism if and only if surjective