Reputation
50,085
Next tag badge:
96/100 score
25/20 answers
Badges
2 65 139
Impact
~477k people reached

10h
comment Classifying Covering Spaces using First Cohomology
I asked a related question many years ago.
1d
comment Is composition of regular epimorphisms always regular?
No, it is false even there. See exercise 5(c) here.
1d
comment Is composition of regular epimorphisms always regular?
Well, strong epimorphisms are always composable, so the hypothesis that regular epi = strong epi just transfers that property to regular epimorphisms. I do not believe that regular epimorphisms are composable in general.
1d
comment A Compact Hausdorff Space with no Manifold Structure?
For some strange values of "nice"...
1d
comment Collective name for algebraic structures
Normal subgroups and submodules are examples of normal subobjects (in the sense of category theory). Ideals of rings don't fit into the category-theoretic picture so well. I suppose you could call all of them "kernels".
1d
answered Converse of realisation lemma for bisimplicial sets
2d
comment Day convolution intuition
Actually, the category of open subsets has two obvious monoidal structures: intersection and union. Day convolution with respect to intersection gives the cartesian product.
2d
comment subobject classifier for partial orders
A cartesian closed category with equalisers and subobject classifiers is an elementary topos, but $\mathbf{Poset}$ is not.
Feb
10
answered Adjoint pair of functors and cogenerator elements
Feb
10
revised Adjoint pair of functors and cogenerator elements
deleted 3 characters in body
Feb
10
comment Errata in Prof. Rotman AIHA book about projectives in the chain complex category
No, there is no need to add anything to my last assertion. There is a notion of projective object in any category, and coproducts of projective objects – whenever they exist – are automatically projective.
Feb
9
answered Errata in Prof. Rotman AIHA book about projectives in the chain complex category
Feb
9
comment Errata in Prof. Rotman AIHA book about projectives in the chain complex category
@TobiasKildetoft The embedding theorem does not guarantee the preservation of infinite direct sums. If it did, then every abelian category with infinite direct sums would satisfy AB4.
Feb
9
awarded  group-theory
Feb
8
comment Is the category of monoids cartesian closed? Why?
Did you read the links you were given at MO?
Feb
7
comment Does $\operatorname{Spec}$ preserve pushouts?
It does not in general, but it does in this case. Compute explicitly.
Feb
7
comment Correct definition of model category
I'm not aware of any results that genuinely require functorial factorisation – however, doing without is sometimes a lot harder. See also here and here.
Feb
6
comment Is there a reasonable Grothendieck topology on the category of modules over a ring?
Incidentally, in the case of vector spaces over a field, the regular topology coincides with the topology in which only the maximal sieves cover.
Feb
6
comment Does $\operatorname{Spec}$ preserve pushouts?
The same example works.
Feb
6
revised Does $\operatorname{Spec}$ preserve pushouts?
added 83 characters in body