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2d
revised $\mathfrak{Top}$ and injective objects
edited tags
2d
answered $\mathfrak{Top}$ and injective objects
2d
comment About certain regular epimorphisms in a Grothendieck Topos
Probably. I don't remember.
Jan
22
comment SupLat and InfLat
Well, there is the obvious inclusion and there is the non-obvious inclusion, obtained by composing with the isomorphism.
Jan
22
comment Connecting morphism in an abelian category
There is no need to bring in any model structure. For some reason homological algebra is very nice.
Jan
21
comment what does Homotopy Tell?
Any two real-valued functions are homotopic. So homotopy tells you nothing in this case.
Jan
21
comment Relating categorical properties of arrows
"Section" (resp. "retraction") is another word for "split monomorphism" (resp. "split monomorphism").
Jan
21
comment SupLat and InfLat
Isomorphic categories are in particular equivalent. There is no contradiction.
Jan
21
comment The Kahler differential is zero
But $A$ is a finite-dimensional $K$-vector space, so how could $K_i$ possibly fail to be a finite-dimensional $K$-vector space?
Jan
21
comment Connecting morphism in an abelian category
You can construct the connecting morphism by using the mapping cone. For instance, see Lemma 9.1.20 in my notes.
Jan
21
comment Do hom-sets really live in the category Set?
There is no problem with terminal objects: they are the singletons. At any rate, whether or not we have urelements makes no difference in a precise technical sense: see here.
Jan
20
comment Do hom-sets really live in the category Set?
Surely it's obvious that sets with urelements don't pose any problems?
Jan
20
comment Proving the snake lemma without a diagram chase
There are many ways to do it. Another way is to use the mapping cone construction.
Jan
20
comment Relating categorical properties of arrows
Monadicity does not imply that every monomorphism is regular.
Jan
19
comment What's the difference between cohomology theories of varieties and topological spaces
The comparison is not entirely fair. For instance, the cohomology of quasicoherent sheaves on varieties should not be compared to, say, singular cohomology with constant coefficients but rather a cohomology theory with local coefficients (e.g. sheaf cohomology).
Jan
18
comment $A$ and $B$ are connected subsets in a metric space X. Prove at least one of $ A\cup B $ or $ A\cap B $ is connected.
For the purposes of this question it seems necessary to take $\emptyset$ to be connected.
Jan
17
comment Abelian categories with tensor product
See also here.
Jan
17
revised Abelian categories with tensor product
edited tags
Jan
17
comment What's the “real” reason a finite map has finite fibers?
Of course, here we are using the fact that the class of finite morphisms is closed under base change.
Jan
17
comment Is it possible to characterize the theory of Integral domains with first-order logic alone ?
It is standard to have the axiom $0 \ne 1$ in the definition of integral domains.