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10h
revised Euler characteristic, genus and cohomology: a deep connection?
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11h
revised Existence of projectives in the category of torsion abelian groups
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22h
comment Are there some reference books or handbooks on homology and homotopy groups of every manifold which has been calculated?
Crossposted on MO.
1d
comment tensor product and commutation, category theoretical argument
You could probably use the fact that filtered categories are sifted.
1d
comment non-abelian Galois cohomology
In [Cohomologie non-abélienne, Ch. III §4], Giraud describes an extended exact sequence of the desired form for short exact sequences satisfying a special condition. But I do not know any of the details.
1d
comment What does $C_{-1}(X)$ mean?
If $X$ is a simplicial complex (resp. topological space) and $C_{\bullet} (X)$ is the simplicial (resp. singular) complex, then one typically defines $C_n (X) = 0$ for $n < 0$.
2d
awarded  Good Question
2d
comment what is the name of this operation?
It's called currying.
Nov
23
revised Is the Zariski Topology
edited tags
Nov
22
comment Homotopy equivalence of pushouts of topological spaces
Sorry, I mean this one instead.
Nov
22
comment Homotopy equivalence of pushouts of topological spaces
possible duplicate of Homotopy equivalence of two different gluings of $B^n$ and an arbitrary space $X$
Nov
22
answered Gpd as a presheaf category
Nov
20
comment Equivalent definitions of regular categories?
It's very simple: under (1) or (2), the pullback of a regular/extremal epimorphism is regular/extremal, so (regular/extremal epi, mono)-factorisations are preserved by pullback, hence images are preserved by pullback.
Nov
20
comment Equivalent definitions of regular categories?
Strange, I think that the obvious direction is that (2) implies (4). At least if you go via (1).
Nov
20
comment Equivalent definitions of regular categories?
Well, isn't (2) just a way of making (4) + cartesian precise?
Nov
20
answered Can the underlying set functor corresponding to an algebraic theory always be viewed as a model of that theory?
Nov
20
comment Is $\mathbb{Z}$ the initial rook?
Oh, actually I was thinking of the other absorption axiom, $0 x = 0$, because then there is no restriction on the endomaps.
Nov
20
comment Equivalent definitions of regular categories?
(1) and (2) are equivalent. Every extremal epi is regular: take its (regular epi, mono)-factorisation and observe that the monomorphism part must be an isomorphism.
Nov
20
comment Is $\mathbb{Z}$ the initial rook?
Isn't this the structure you get when you look at the set of endomaps of a group, with $+$ being the pointwise group operation and juxtaposition being composition?
Nov
20
comment Equivalent definitions of regular categories?
(3) is stronger than the others because coequalisers don't have to exist in general. (4) is weaker than the others because finite limits don't have to exist in general.