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Karol Szumiło's user avatar
Karol Szumiło's user avatar
Karol Szumiło
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87 Answers

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37 votes
Accepted

Brown representability for non-connected spaces

22 votes
Accepted

Dimension in CW-approximation

21 votes

Conceptual reason why the sign of a permutation is well-defined?

16 votes
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Cocontinuous product-preserving functor between Grothendieck toposes

16 votes
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On a weaker version of homotopy equivalence between topological spaces

15 votes
Accepted

Can homotopy pullbacks of spaces be checked on fibers?

14 votes
Accepted

When are (weak) homotopy equivalence testable on open covers?

14 votes
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Constructing a "geometric" model structure on Cat by localizing the "categorical" model structure

14 votes
Accepted

Unpointed Brown representability theorem

12 votes
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Reference for "lax monoidal functors" = "monoids under Day convolution"

12 votes
Accepted

Is the localisation of a product of categories the product of the localisation?

12 votes
Accepted

Are Brown representable functors determined by restriction to finite complexes?

12 votes
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When do colimits agree with homotopy colimits?

11 votes

Semi-simplicial versus simplicial sets (and simplicial categories)

11 votes

Are categories of fibrant objects idempotent complete?

10 votes

Extending Kan fibrations, without using minimal fibrations

10 votes

Enriched locally presentable categories

10 votes
Accepted

Can a weak fibration category be non saturated?

10 votes
Accepted

Relative version of Quillen's theorem A

10 votes

A homology theory which satisfies Milnor's additivity axiom but not the direct limit axiom?

9 votes
Accepted

Is the homotopy category of a ring also the derived category of another ring?

9 votes

A more natural proof of Dold-Kan?

9 votes
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Characterization of Tychonoff spaces in terms of open sets

9 votes
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When does localization preserve homotopy type of classifying spaces?

9 votes
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Is there a model structure on (strict?) Monoidal Categories?

8 votes
Accepted

Homotopy pullbacks/relative homotopy groups vs homotopy pushouts/relative homology groups

8 votes
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Enriched cartesian closed categories

8 votes
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What is the relation between a ''homotopy fiber bundle'' and a Serre fibration?

8 votes
Accepted

Strict categorical localization is automatically a "2-localization"?

8 votes
Accepted

When is a cube of cofibrations are "lattice"?

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