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15
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Why do $S^1 \wedge - $ and $Maps(S^1,-)$ form a Quillen adjunction?

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#algebraic-topology #homotopy-theory #model-categories
281
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In what sense are (co)fibrant replacements "better"?

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#homotopy-theory #model-categories
215
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A fibration $p : E \rightarrow X$ is trivial iff $p$ is a homotopy equivalence

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#algebraic-topology #homotopy-theory #simplicial-stuff #model-categories
232
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Quillen equivalence between sSet (Joyal's model structure) and sSetCat (Bergner's one)

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#category-theory #proof-explanation #simplicial-stuff #higher-category-theory #model-categories
242
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Definiton of the beta in Lurie's HTT

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#category-theory #definition #model-categories #enriched-category-theory
106
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The choice of cofibrant approximation is contractible

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#category-theory #simplicial-stuff #model-categories
308
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Do Homotopy limits commute with right Quillen functors

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#algebraic-topology #category-theory #homotopy-theory #simplicial-stuff #model-categories
204
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The cofibration from the $\textbf{Top}$'s model category

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#homotopy-theory #model-categories
274
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Necessary conditions for a Reedy fibrant diagram

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#algebraic-topology #homotopy-theory #simplicial-stuff #model-categories
98
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How far are functors valued in Ho(Cat) from pseudofunctors?

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#category-theory #model-categories #bicategories
236
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Left Homotopy is an Equivalence Relation

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#homotopy-theory #model-categories
256
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Are all isomorphisms contained in the class of weak equivalences?

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#category-theory #model-categories
695
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How can I understand maps out of a limit or into a colimit?

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#category-theory #simplicial-stuff #model-categories
182
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Factorization axiom for model categories

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#category-theory #model-categories
317
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model structure on the arrow category

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#category-theory #model-categories

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