31

Answers
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7
Reference for “lax monoidal functors” = “monoids under Day convolution”
5
Can one make the category of pairs of topological spaces a model category?
1
Does the Monoid Axiom hold for k-spaces?
1
Reedy model structures on oplax limits
3
Local finality condition (for re-indexing parameterized colimits)
6
Loop space of a category
3
Injective objects in Mor(Ab)
2
Does the following categorial sum preserve weak equivalences?
5
unpointed brown representability theorem
13
Brown representability for non-connected spaces
6
Alternative characterization of homotopy equivalence
1
General gluing theorem for adjunction spaces
5
Is it possible to define the notion of a localization of a category without reference to a set of morphisms, $S$?
2
Evaluation functors and injective model structure on diagram categories
2
What properties make $[0,1]$ a good candidate for defining fundamental groups?
4
Sheaf cohomology invariant of weak homotopy type?
3
Exact sequences in homotopy categories
8
When is a cube of cofibrations are “lattice”?
6
mapping spaces of diagrams
2
When do functors induce monadic adjunctions of presheaf categories
4
Suspension of an excisive pair
7
What is the relation between a ‘'homotopy fiber bundle’' and a Serre fibration?
1
The boundary map of Kan simplicial sets
3
Two kinds of equivalence: conjugate vs. isomorphic objects
6
Semi-simplicial versus simplicial sets (and simplicial categories)
5
Strict categorical localization is automatically a “2-localization”?
2
Localizing at homotopy equivalences
5
Characterization of Tychonoff spaces in terms of open sets
3
geometric realization on $\mathbf{sTop}$
3
On the barycentric subdivision of a poset
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