$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$
9 Large $\infty $-Categories
Structure
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Section 9.1: Filtered $\infty $-Categories
- Subsection 9.1.1: Filtered $\infty $-Categories
- Subsection 9.1.2: Local Characterization of Filtered $\infty $-Categories
- Subsection 9.1.3: Fibrations over Filtered $\infty $-Categories
- Subsection 9.1.4: Digression: Commutation of Limits and Colimits
- Subsection 9.1.5: Filtered Colimits of Spaces
- Subsection 9.1.6: Filtered Colimits of Simplicial Sets
- Subsection 9.1.7: Approximation by Simplicial Subsets
- Subsection 9.1.8: Approximation by Partially Ordered Sets
- Subsection 9.1.9: Finitary Functors
- Subsection 9.1.10: Filtered Colimits of $\infty $-Categories
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Section 9.2: Compact Objects and Ind-Completion
- Subsection 9.2.1: Ind-Completion
- Subsection 9.2.2: Compact Objects
- Subsection 9.2.3: Recognition of Ind-Completions
- Subsection 9.2.4: Flat Functors
- Subsection 9.2.5: Exact Functors
- Subsection 9.2.6: Compactly Generated $\infty $-Categories
- Subsection 9.2.7: Finiteness Conditions on Spaces
- Subsection 9.2.8: Finiteness Conditions on $\infty $-Categories
- Subsection 9.2.9: Transitivity of $\operatorname{Ind}$-Completion
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Section 9.3: Local Objects and Factorization Systems
- Subsection 9.3.1: Digression: Transfinite Composition
- Subsection 9.3.2: Weakly Local Objects
- Subsection 9.3.3: The Small Object Argument
- Subsection 9.3.4: Lifting Problems in $\infty $-Categories
- Subsection 9.3.5: Weak Factorization Systems
- Subsection 9.3.6: Orthogonality
- Subsection 9.3.7: Uniqueness of Factorizations
- Subsection 9.3.8: Factorization Systems
- Section 9.4: Truncated Objects of $\infty $-Categories