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As suggested I repost my comment as an answer. The paper Adámek, Borceux, Lack, Rosický, A classification of accessible categories addresses exactly these types of questions. In particular, Section 3 …

The results on homotopy invariance of the geometric realization of simplicial spaces go back at least to May's The Geometry of Iterated Loop Spaces, although he doesn't explicitly mention model catego …

There are a few papers that cite Tornehave's preprint entitled On BSG and the symmetric groups apparently dating from early 70s or late 60s. Google search reveals very little. Does anyone have access …

$\require{AMScd}$I don't know a reference but the proof is easy enough. Form homotopy pullback squares \begin{CD} Fu @>>> Ff @>>> A \\ @VVV @VVV @V{u}VV \\ * @>>> Fg @>>> P @>>> B \\ @. @VVV @VVV @VV …

The short answer is no. If you take the semi-simplicial set $X$ with one $0$-simplex and no higher simplices, then it has fillers for all inner horns (because it has no inner horns) but clearly does n …

You may be thinking of Johnson, Mark W. On modified Reedy and modified projective model structures. Theory Appl. Categ. 24 (2010), No. 8, 179–208. but his constructions (Definitions 3.3 and 5.2) hav …

This observation appears already in Day's thesis as Example 3.2.2. For some reason it is only stated for commutative monoids and symmetric (pro)monoidal functors and only as a correspondence of object …

I believe that the standard barycentric subdivision functor $\mathrm{Sd} \colon \mathsf{sSet} \to \mathsf{sSet}$ factors through cubical sets with connections. We define a functor $S \colon \Delta \to …

For any small category $J$, the colimit functor $\mathsf{Set}^J \to \mathsf{Set}$ preserves colimits. It preserves finite limits if and only if $J$ is filtered and it preserves finite products if and …

The theory is also developed further in two papers by Borceux, Quinteiro and Rosický: Enriched accessible categories MR1419612 and A theory of enriched sketches MR1624638. In the second one they say t …

This is far from a comprehensive answer, but since you ask for references, here are two. The result for simplicial sets is obtained by an explicit computation in Appendix H of Joyal's The Theory of Q …

I was quite sure that this was explicitly written down by Rădulescu-Banu or by Hirschhorn, but I cannot find this exact statement. However, this follows directly by combining Theorems 7.5.10 and 7.6. …

No. Let $X$ be an uncountable set and consider $I^X$ with the product topology. Then the inclusion $\{ 0 \} \to I^X$ is a closed embedding between (strongly) contractible spaces which are therefore mi …