Here are some extra references. (Maybe this is easier to read: link)

```
├── Complete Segal Spaces
│ ├── [BC, 10 Pages] Equivariant Complete Segal Spaces.pdf
│ ├── [Brito, 26 Pages] Segal Objects and the Grothendieck Construction.pdf
│ ├── [Osborne, 25 Pages] Decomposing the Classifying Diagram in Terms of Classifying Spaces of Groups.pdf
│ ├── [Rasekh, 17 Pages] A Model for the Higher Category of Higher Categories.pdf
│ ├── [Rasekh, 44 Pages] Complete Segal Objects.pdf
│ ├── [Rasekh, 478 Pages] A Theory of Elementary Higher Toposes.pdf
│ ├── [Rasekh, 61 Pages] Introduction to Complete Segal Spaces.pdf
│ ├── [Rasekh, 75 Pages] Yoneda Lemma for Simplicial Spaces.pdf
│ ├── [Rasekh, 81 Pages] Cartesian Fibrations and Representability.pdf
│ ├── [Stenzel, 21 Pages] Univalence and Completeness of Segal Objects.pdf
│ └── [Stenzel, 26 Pages] Bousfield-Segal Spaces.pdf
├── Elementary ∞-Topoi
│ ├── [Rasekh, 10 Pages] Yoneda Lemma for Elementary Higher Toposes.pdf
│ ├── [Rasekh, 30 Pages] Filter Quotients and Non-Presentable (∞,1)-Toposes.pdf
│ ├── [Rasekh, 40 Pages] A Theory of Elementary Higher Toposes.pdf
│ ├── [Rasekh, 51 Pages] Every Elementary Higher Topos Has a Natural Number Object.pdf
│ └── [Rasekh, 84 Pages] An Elementary Approach to Truncations.pdf
├── Enriched (∞,1)-Categories
│ ├── [AMR, 68 Pages] Factorization Homology of Enriched ∞-Categories.pdf
│ ├── [GH, 100 Pages] Enriched ∞-Categories via Non-Symmetric ∞-Operads.pdf
│ ├── [Haugseng, 29 Pages] Bimodules and Natural Transformations for Enriched ∞-Categories.pdf
│ └── [Haugseng, 52 Pages] Rectification of Enriched Infinity-Categories.pdf
├── General References
│ ├── [AL, 26 Pages] Exponentiable Higher Toposes.pdf
│ ├── [Arctaedius, 38 Pages] Grothendieck's Homotopy Hypothesis and the Homotopy Theory of Homotopy Theories.pdf
│ ├── [Bergner, 13 Pages] A Survey of (∞, 1)-Categories.pdf
│ ├── [Bergner, 287 Pages] The Homotopy Theory of (∞,1)-Categories.pdf
│ ├── [Bergner, 29 Pages] A Survey of Models for (∞,n)-Categories.pdf
│ ├── [Bergner, 39 Pages] Workshop on the Homotopy Theory of Homotopy Theories.pdf
│ ├── [Camarena, 45 Pages] A Whirlwind Tour of the World of (∞,1)-Categories.pdf
│ ├── [Clough, 35 Pages] An Outline of the Theory of (∞,1)-Categories.pdf
│ ├── [Dorn, 99 Pages] Basic concepts in homotopy theory.pdf
│ ├── [HF, 148 Pages] The Homotopy Theory of (∞,1)-Categories.pdf
│ ├── [Mazel-Gee, 26 Pages] The Zen of ∞-Categories.pdf
│ ├── [Porter, 37 Pages] 𝒮-categories, 𝒮-groupoids, Segal categories and quasicategories.pdf
│ ├── [Porter, 54 Pages] Spaces as ∞-groupoids.pdf
│ ├── [Porter, 759 Pages] The Crossed Menagerie.pdf
│ ├── [Schommer-Pries, 65 Pages] Dualizability in Low-Dimensional Higher Category Theory.pdf
│ └── [Simpson, 653 Pages] Homotopy Theory of Higher Categories.pdf
├── Model (∞,1)-Categories
│ ├── [LM, 21 Pages] From Fractions to Complete Segal Spaces.pdf
│ ├── [Mazel-Gee, 16 Pages] A User's Guide to Co⧸Cartesian Fibrations.pdf
│ ├── [Mazel-Gee, 20 Pages] Quillen Adjunctions Induce Adjunctions of Quasicategories.pdf
│ ├── [Mazel-Gee, 26 Pages] The Universality of the Rezk Nerve.pdf
│ ├── [Mazel-Gee, 29 Pages] Model ∞-Categories II: Quillen Adjunctions.pdf
│ ├── [Mazel-Gee, 34 Pages] Model ∞-Categories III: The Fundamental Theorem.pdf
│ ├── [Mazel-Gee, 41 Pages] All About the Grothendieck Construction.pdf
│ ├── [Mazel-Gee, 43 Pages] Hammocks and Fractions in Relative ∞-Categories.pdf
│ ├── [Mazel-Gee, 528 Slides] Goerss–Hopkins obstruction theory for ∞-Categories.pdf
│ ├── [Mazel-Gee, 545 Pages] Goerss–Hopkins obstruction theory via model ∞-categories.pdf
│ ├── [Mazel-Gee, 54 Pages] Goerss–Hopkins Obstruction Theory for ∞-Categories.pdf
│ ├── [Mazel-Gee, 66 Pages] Model ∞-Categories I: Some Pleasant Properties of the ∞-Category of Simplicial Spaces.pdf
│ └── [Mazel-Gee, 6 Pages] 𝔼_∞ Automorphisms of Motivic Morava E-Theories.pdf
├── Other Models
│ ├── Batanin ∞-Categories
│ │ └── [Ara, 168 Pages] Sur les ∞-groupoïdes de Grothendieck et une variante ∞-catégorique.pdf
│ ├── Grothendieck–Maltsiniotis ∞-Categories
│ │ ├── [AL, 65 Pages] The Folk Model Category Structure on Strict ω-Categories Is Monoidal.pdf
│ │ ├── [AM, 123 Pages] A Quillen's Theorem A for Strict ∞-Categories II: The ∞-Categorical Proof.pdf
│ │ ├── [AM, 227 Pages] Join and Slices for Strict ∞-Categories.pdf
│ │ ├── [AM, 25 Pages] The Brown–Golasinski Model Structure on Strict ∞-Groupoids Revisited.pdf
│ │ ├── [AM, 42 Pages] Comparison of the n-Categorical Nerves.pdf
│ │ ├── [AM, 51 Pages] A Quillen's Theorem A for Strict ∞-Categories I: The Simplicial Proof.pdf
│ │ ├── [AM, 68 Pages] The Homotopy Type of the ∞-Category Associated to a Simplicial Complex.pdf
│ │ ├── [AM, 92 Pages] Towards a Thomason Model Structure on the Category of Strict n-Categories.pdf
│ │ ├── [Ara, 22 Pages] On Homotopy Types Modelized by Strict ∞-Groupoids.pdf
│ │ ├── [Ara, 22 Pages] Strict ∞-Groupoids Are Grothendieck ∞-Groupoids.pdf
│ │ ├── [Ara, 33 Pages] A Quillen Theorem B for Strict ∞-Categories.pdf
│ │ ├── [Ara, 41 Pages] The Groupoidal Analogue Θ to Joyal's Category Θ Is a Test Category.pdf
│ │ └── [Ara, 58 Pages] On the Homotopy Theory of Grothendieck ∞-Groupoids.pdf
│ ├── Miscellany
│ │ ├── [CL, 61 Pages] Weak ∞-Categories via Terminal Coalgebras.pdf
│ │ ├── [Harpaz, 69 Pages] Quasi-Unital ∞-Categories.pdf
│ │ ├── [LM, 68 Pages] Linear Quasi-Categories as Templicial Modules.pdf
│ │ └── [Nikolaus, 26 Pages] Algebraic Models for Higher Categories.pdf
│ ├── Relative Categories
│ │ ├── [BK, 19 Pages] n-Relative Categories.pdf
│ │ ├── [BK, 27 Pages] Relative Categories: Another Model for the Homotopy Theory of Homotopy Theories.pdf
│ │ ├── [BK, 3 Pages] A Thomason-Like Quillen Equivalence Between Quasi-Categories and Relative Categories.pdf
│ │ ├── [BK, 5 Pages] In the Category of Relative Categories the Rezk Equivalences Are Exactly the DK-equivalences.pdf
│ │ └── [Meier, 21 Pages] Fibration Categories Are Fibrant Relative Categories.pdf
│ └── Topological Categories
│ ├── [Amrani, 22 Pages] A Model Structure on the Category of Topological Categories.pdf
├── Parametrised (∞,1)-Categories
│ ├── [BDGNS, 11 Pages] Parametrized Higher Category Theory and Higher Algebra: A General Introduction.pdf
│ ├── [BDGNS, 23 Pages] Parametrized Higher Category Theory and Higher Algebra: Exposé I -- Elements of Parametrized Higher Category Theory.pdf
│ ├── [Nardin, 21 Pages] Parametrized Higher Category Theory and Higher Algebra: Exposé IV -- Stability With Respect to an Orbital ∞-Category.pdf
│ ├── [Shah, 81 Pages] Parametrized Higher Category Theory and Higher Algebra: Exposé II - Indexed Homotopy Limits and Colimits.pdf
│ └── [Shah, 86 Slides] Parametrized Higher Category Theory.pdf
├── Quasicategories
│ ├── [AL, 26 Pages] Exponentiable Higher Toposes.pdf
│ ├── [Beardsley, 78 Pages] Coalgebraic Structure and Intermediate Hopf–Galois Extensions of Thom Spectra in Quasicategories.pdf
│ ├── [Berman, 13 Pages] On Lax Limits in ∞-Categories.pdf
│ ├── [BG, 11 Pages] On the Fibrewise Effective Burnside ∞-Category.pdf
│ ├── [BM, 30 Pages] Spectral Sequences in (∞,1)-Categories.pdf
│ ├── [BS, 18 Pages] Fibrations in ∞-Category Theory.pdf
│ ├── [BV, 267 Pages] Homotopy Invariant Algebraic Structures On Topological Spaces.djvu
│ ├── [Campbell, 3 Pages] A Counterexample in Quasi-Category Theory.pdf
│ ├── [Cisinski, 204 Pages] Algèbre Homotopique et Catégories Supérieures.pdf
│ ├── [Cisinski, 446 Pages] Higher Categories and Homotopical Algebra.pdf
│ ├── [Cisisnki, 57 Pages] Catégories Supérieures et Théorie des Topos.pdf
│ ├── [DS, 46 Pages] Mapping Spaces in Quasi-Categories.pdf
│ ├── [Fiore, 24 Pages] Quasicategorical Adjunctions.pdf
│ ├── [GR, 11 Pages] Simplified HTT 4.3.2.15.pdf
│ ├── [GR, 85 Pages] Some Higher Algebra.pdf
│ ├── [Gregoric, 21 Pages] Gregoric Blitzkrieg.pdf
│ ├── [Groth, 77 Pages] A Short Course on ∞-Categories.pdf
│ ├── [Harpaz, 116 Pages] Little Cube Algebras and Factorisation Homology.pdf
│ ├── [Harpaz, 7 Pages] Limits, colimits and adjunctions in ∞-categories.pdf
│ ├── [Haugseng, 12 Pages] On (Co)ends in ∞-Categories.pdf
│ ├── [Haugseng, 28 Pages] A Fibrational Mate Correspondence for ∞-Categories.pdf
│ ├── [Haugseng, 87 Pages] Introduction to ∞-Categories.pdf
│ ├── [HH, 684 Pages] Higher Categories I & II
│ │ ├── 0 [Hebestreit, 13 Pages] A Fairytale.pdf
│ │ ├── 10 [Hebestreit, 11 Pages] Fat and Thin Slices.pdf
│ │ ├── 11 [Hebestreit, 43 Pages] Cartesian Fibrations.pdf
│ │ ├── 12 [Hebestreit, 121 Pages] Straightening and Unstraightening.pdf
│ │ ├── 12' [HH, 53 Pages] Straightening and Unstraightening (Heuts's Notes).pdf
│ │ ├── 13 [Hebestreit, 14 Pages] Homotopy Colimits.pdf
│ │ ├── 14 [Hebestreit, 10 Pages] Simplicial Model Categories.pdf
│ │ ├── 15 [Hebestreit, 35 Pages] Yoneda's Lemma, Adjunctions and (Co)Limits.pdf
│ │ ├── 1 [Hebestreit, 37 Pages] Categories.pdf
│ │ ├── 2 [Hebestreit, 25 Pages] Simplicial Sets.pdf
│ │ ├── 3 [Hebestreit, 10 Pages] Quasicategories.pdf
│ │ ├── 4 [Hebestreit, 53 Pages] Simplicial Categories.pdf
│ │ ├── 5 [Hebestreit, 38 Pages] Simplicial Homotopy Theory.pdf
│ │ ├── 6 [Hebestreit, 57 Pages] Quasicategories and Anima.pdf
│ │ ├── 7 [Hebestreit, 67 Pages] Equivalences, Equivalences, Equivalences.pdf
│ │ ├── 8 [Hebestreit, 9 Pages] A Fairytale.pdf
│ │ └── 9 [Hebestreit, 88 Pages] Localisations and Model Categories.pdf
│ ├── [Hinich, 111 Pages] Lectures on ∞-Categories.pdf
│ ├── [Joyal, 244 Pages] Notes on Quasi-Categories.pdf
│ ├── [Joyal, 350 Pages] The Theory of Quasi-Categories and its Applications II.pdf
│ ├── [Joyal, 479 Pages] The Theory of Quasi-Categories.pdf
│ ├── [Lejay, 139 Pages] Algèbres à Factorisation et Topos Supérieurs Exponentiables.pdf
│ ├── [Lurie, 60 Pages] On ∞-Topoi.pdf
│ ├── [Lurie, 841 Pages] Kerodon.pdf
│ ├── [Lurie, 949 Pages] Higher Topos Theory.pdf
│ ├── [Lysenko, 208 Pages] Lysenko's comments to Gaitsgory–Rozenblyum.pdf
│ ├── [Morel, 118 Pages] ∞-Categories.pdf
│ ├── [Nguyen, 94 Pages] Theorems in Higher Category Theory and Applications.pdf
│ ├── [NRS, 21 Pages] Adjoint Functor Theorems for ∞-Categories.pdf
│ ├── [Porta, 100 Pages] Derived formal moduli problems.pdf
│ ├── [Rezk, 11 Pages] Degenerate Edges of Cartesian Fibrations are Cartesian Edges.pdf
│ ├── [Rezk, 175 Pages] Stuff About Quasicategories.pdf
│ ├── [Rezk, 50 Pages] Toposes and homotopy toposes.pdf
│ ├── [Riehl, 20 Pages] Quasi-Categories as (∞,1)-Categories.pdf
│ ├── [Riehl, 292 Pages] Categorical homotopy theory.pdf
│ ├── [Riehl, 9 Pages] Associativity Data in an (∞,1)-Category.pdf
│ ├── [Rovelli, 38 Pages] Weighted Limits in an (∞,1)-Category.pdf
│ ├── [RS, 151 Pages] Notes on Higher Categories.pdf
│ ├── [RV, 33 Pages] Completeness Results for Quasi-Categories of Algebras, Homotopy Limits, and Related General Constructions.pdf
│ ├── [Stevenson, 12 Pages] Stability for Inner Fibrations Revisited.pdf
│ ├── [Tanaka, 14 Pages] Functors (Between ∞-Categories) That Aren't Strictly Unital.pdf
│ ├── [Thanh, 46 Pages] Quasicategories.pdf
│ ├── [Wong, 83 Pages] The Grothendieck construction in enriched, internal and ∞-Category Theory.pdf
│ ├── [Zsámboki, 31 Pages] A summary of higher topos theory.pdf
│ └── [無, 5 Pages] HTT ToC.pdf
├── Simplicial Categories
│ ├── [Bergner, 16 Pages] A model category structure on the category of simplicial categories.pdf
│ ├── [Bergner, 22 Pages] Complete Segal Spaces Arising From Simplicial Categories.pdf
│ ├── [Bergner, 40 Pages] Three models for the homotopy theory of homotopy theories.pdf
│ ├── [Cordier, 21 Pages] Sur la notion de diagramme homotopiquement cohérent.pdf
│ ├── [CP, 26 Pages] Vogt's Theorem on Categories of Homotopy Coherent Diagrams.pdf
│ ├── [CP, 54 Pages] Homotopy Coherent Category Theory.pdf
│ ├── [DS, 29 Pages] Rigidification of Quasi-Categories.pdf
│ ├── [DS, 64 Pages] Mapping Spaces in Quasi-Categories.pdf
│ ├── [Hinich, 23 Pages] Homotopy Coherent Nerve in Deformation Theory.pdf
│ ├── [HK, 14 Pages] Mapping Spaces in Homotopy Coherent Nerves.pdf
│ ├── [Joyal, 66 Pages] Quasi-Categories vs Simplicial Categories.pdf
│ ├── [Riehl, 16 Pages] On the Structure of Simplicial Categories Associated to Quasi-Categories.pdf
│ ├── [Riehl, 26 Pages] Homotopy Coherent Structures.pdf
│ ├── [Riehl, 292 Pages] Categorical Homotopy Theory.pdf
│ └── [Riehl, 7 Pages] Understanding the Homotopy Coherent Nerve.pdf
├── Unicity
│ ├── [Bergner, 16 Pages] Equivalence of Models for Equivariant (∞,1)-Categories.pdf
│ ├── [BS, 47 Pages] On the Unicity of the Homotopy Theory of Higher Categories.pdf
│ ├── [JT, 49 Pages] Quasi-Categories vs Segal Spaces.pdf
│ ├── [Riehl, 58 Pages] Seminar Notes on the Barwick–Schommer–Pries Unicity Theorem.pdf
│ └── [Toën, 32 Pages] Vers une axiomatisation de la théorie des catégories supérieures.pdf
└── Un⧸Straightening
├── [AF, 89 Pages] Fibrations of ∞-Categories.pdf
├── [BGN, 19 Pages] Dualizing Cartesian and Cocartesian Fibrations.pdf
├── [BS, 18 Pages] Fibrations in ∞-Category Theory.pdf
├── [Campbell, 31 Slides] A modular proof of the straightening theorem.pdf
├── [GHN, 42 Pages] Lax Colimits and Free Fibrations in ∞-Categories.pdf
├── [GR, 85 Pages] Some Higher Algebra.pdf
├── [Hebestreit, 121 Pages] Straightening and Unstraightening.pdf
├── [HH, 53 Pages] Straightening and Unstraightening (Heuts's Notes).pdf
├── [HM, 17 Pages] Left Fibrations and Homotopy Colimits II.pdf
├── [HM, 27 Pages] Left Fibrations and Homotopy Colimits.pdf
├── [Mazel-Gee, 16 Pages] A User's Guide to (Co)Cartesian Fibrations.pdf
├── [Mazel-Gee, 41 Pages] All About the Grothendieck Construction.pdf
├── [Noel, 1 Page] Cartesian Model Structure.pdf
├── [PK, 43 Pages] Straightening and Unstraightening.pdf
├── [Richardson, 14 Pages] Mapping Spaces and Straightening-Unstraightening.pdf
├── [Ruit, 71 Pages] Grothendieck constructions in higher category theory.pdf
├── [Stevenson, 41 Pages] Model Structures for Correspondences and Bifibrations.pdf
├── [Stevenson, 49 Pages] Covariant Model Structures and Simplicial Localization.pdf
└── [Wong, 83 Pages] The Grothendieck Constructionin Enriched, Internal and ∞-Category Theory.pdf
```

homotopy categoryof $\mathfrak{C}$. (The 'usually' I cannot precisely justify.) $\endgroup$