User Karol Szumiło

8 votes

Accepted

When is a cube of cofibrations are "lattice"?

answered Feb 22, 2012 at 17:59

7 votes

Accepted

Sheaf cohomology invariant of weak homotopy type?

answered Mar 13, 2012 at 21:24

7 votes

Is it possible to define the notion of a localization of a category without reference to a set of morphisms, $S$?

answered Apr 6, 2012 at 6:45

7 votes

Can one make the category of pairs of topological spaces a model category?

answered Apr 28, 2013 at 7:18

7 votes

Accepted

When does simplicial localization commute with functor categories?

answered Jul 4, 2014 at 19:40

7 votes

Accepted

Is the category of $G$-spaces a model category?

answered Aug 6, 2014 at 16:30

7 votes

Accepted

Do finite simplicial sets jointly detect isomorphisms in the homotopy category?

answered Oct 12, 2018 at 8:00

6 votes

Accepted

Homotopy pushout independent of factorization and symmetric in cofibration category

answered Jul 17, 2018 at 10:49

6 votes

Affine spaces as algebras for an operad?

answered Jan 25, 2017 at 11:43

6 votes

Accepted

Simple characterization of Postnikov & Whitehead towers?

answered Jan 28, 2017 at 16:04

6 votes

Accepted

Freely adding degeneracies does not change the homotopy type

answered Oct 29, 2014 at 12:33

6 votes

Accepted

recognising weak equivalences of simplicial sets

answered Jan 29, 2015 at 12:57

6 votes

Accepted

Pushouts of equivalences of categories

answered Jul 15, 2014 at 7:49

6 votes

Accepted

Different model structures on Top

answered Nov 9, 2015 at 12:40

6 votes

Accepted

Do homotopy categories of finitely (co)complete quasicategories determine categorical equivalences?

answered Jul 30, 2016 at 10:04

6 votes

Loop space of a category

answered Nov 26, 2012 at 18:30

6 votes

Accepted

mapping spaces of diagrams

answered Feb 15, 2012 at 0:10

6 votes

Alternative characterization of homotopy equivalence

answered Jan 18, 2012 at 18:35

5 votes

What properties make $[0,1]$ a good candidate for defining fundamental groups?

answered Mar 26, 2012 at 14:50

5 votes

Suspension of an excisive pair

answered Jan 5, 2012 at 19:32

5 votes

Two kinds of equivalence: conjugate vs. isomorphic objects

answered Nov 2, 2011 at 20:44

5 votes

General gluing theorem for adjunction spaces

answered May 6, 2012 at 5:59

5 votes

Reedy model structures on oplax limits

answered Jan 31, 2013 at 8:08

5 votes

Accepted

How to simplify the proof of right-properness?

answered Feb 4, 2016 at 12:49

5 votes

Accepted

Can the groupoid completion of a topological category be recovered from its classifying space?

answered Mar 17, 2016 at 1:15

5 votes

Accepted

homotopy tensor product of functors and bar construction

answered Feb 18, 2015 at 20:28

5 votes

Accepted

Does the right adjoint of the category of simplices functor is "homotopicaly inverse" to the category of simplices functor?

answered Aug 17, 2014 at 12:57

5 votes

Functors between simplicial sets and cubical sets with connections

answered Apr 21, 2017 at 14:39

5 votes

Accepted

(Co)limits of locally cartesian closed categories

answered Dec 10, 2017 at 7:15

4 votes

Is the map between mapping spaces, induced by the functor $\vert Sing(-)\vert$ continuous?

answered Jan 16, 2019 at 12:52

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87 Answers

When is a cube of cofibrations are "lattice"?

Sheaf cohomology invariant of weak homotopy type?

Is it possible to define the notion of a localization of a category without reference to a set of morphisms, $S$?

Can one make the category of pairs of topological spaces a model category?

When does simplicial localization commute with functor categories?

Is the category of $G$-spaces a model category?

Do finite simplicial sets jointly detect isomorphisms in the homotopy category?

Homotopy pushout independent of factorization and symmetric in cofibration category

Affine spaces as algebras for an operad?

Simple characterization of Postnikov & Whitehead towers?

Freely adding degeneracies does not change the homotopy type

recognising weak equivalences of simplicial sets

Pushouts of equivalences of categories

Different model structures on Top

Do homotopy categories of finitely (co)complete quasicategories determine categorical equivalences?

Loop space of a category

mapping spaces of diagrams

Alternative characterization of homotopy equivalence

What properties make $[0,1]$ a good candidate for defining fundamental groups?

Suspension of an excisive pair

Two kinds of equivalence: conjugate vs. isomorphic objects

General gluing theorem for adjunction spaces

Reedy model structures on oplax limits

How to simplify the proof of right-properness?

Can the groupoid completion of a topological category be recovered from its classifying space?

homotopy tensor product of functors and bar construction

Does the right adjoint of the category of simplices functor is "homotopicaly inverse" to the category of simplices functor?

Functors between simplicial sets and cubical sets with connections

(Co)limits of locally cartesian closed categories

Is the map between mapping spaces, induced by the functor $\vert Sing(-)\vert$ continuous?