For questions involving one or more categorical dimensions, or involving homotopy coherent categorical structures.

**4**

**0**answers

### What does it mean to say the first Goodwillie derivative of $TC$ is $THH$?

**7**

**1**answer

### Simplicial nerve functor commutes with opposites

**8**

**0**answers

### Is every presentable category a limit of locally finitely-presentable categories and finitary left adjoints?

**6**

**1**answer

### Is a weak functor which strictly preserves horizontal composition and which runs between strict bicategories automatically strict?

**4**

**0**answers

### Minimal infinity categories in the Segal space picture

**9**

**2**answers

### What are the reflective subcategories of the category of presentable categories?

**3**

**1**answer

### 2-morphisms for Bord(n)

**6**

**1**answer

### Is there a relationship between norms/transfers in equivariant homotopy theory and norms in the Tate construction / ambidexterity?

**12**

**1**answer

### What is the coskeleton tower of a quasi-category?

**15**

**2**answers

### How can I functorially dualise in a symmetric monoidal $(\infty,1)$-category with duals?

**4**

**0**answers

### Nonabelian Poincare duality

**2**

**1**answer

### Is the site for cubical sets with connections equivalent to a full subcategory of posets?

**3**

**0**answers

### Which kind of functors preserve the bar-construction?

**2**

**1**answer

### Specifying complexes in quasicategories via squares

**13**

**0**answers

### Localizing $\mathrm{CombModCat}$ at the Quillen equivalences

**3**

**1**answer

### Definition of $(\infty,1)$-category in HoTT [duplicate]

**6**

**2**answers

### Are cofibrations accessible?

**9**

**0**answers

### Is there an “injective version” of the Bergner model structure?

**3**

**0**answers

### What is the structure required to construct this homotopy of maps between mapping cones?

**4**

**0**answers

### Is there a good, general description of morphisms right orthogonal to effective epimorphisms?

**5**

**0**answers

### Applications of spectral Artin representability?

**4**

**0**answers

### Internal van Kampen colimits

**18**

**1**answer

### Spectral algebraic geometry vs derived algebraic geometry in positive characteristic?

**7**

**1**answer

### What is the relationship between $O_G$-parameterized $\infty$-categories and $\infty$-categories enriched in $Top_G$?

**3**

**0**answers

### Calculating the intersection of the saturations of a decreasing sequence of morphisms

**2**

**2**answers

### Spelling out explicitly the data of a two step filtration in terms of pieces and gluing data

**13**

**2**answers

### What kind of category is generated by Cubical type theory?

**5**

**1**answer

### Left split subobject in a $2$-category

**5**

**1**answer

### Explicit expression of the unstraightening functor

**9**

**2**answers

### 2-natural operations on toposes

**14**

**3**answers

### Do combinatorial model categories and Quillen adjunctions model presentable $\infty$-categories?

**8**

**1**answer

### Weak colimits in locally cartesian closed categories

**13**

**1**answer

### Weak complicial sets: Are the morphisms too strict?

**13**

**2**answers

### What is a model category from an $\infty$ point of view?

**8**

**0**answers

### How to define the direct sum of TQFTs $(\infty,1)$-categorically?

**8**

**1**answer

### Gurski's Definition of a strict functor of tricategories

**7**

**1**answer

### Can an enriched functor be expressed as a colimit of representable functors?

**6**

**1**answer

### Is there a general way to turn a 2-monad into a lax-idempotent (a.k.a. KZ) 2-monad?

**10**

**0**answers

### Is every colimit-generator dense in an $\infty$-topos?

**4**

**1**answer

### Kan condition for bar construction

**11**

**2**answers

### Questions about categorification (& combinatorial simplification of the Russian approach to Lusztig's conjectures, in zero & positive characteristic) [closed]

**2**

**1**answer

### When is the derived category $D(A)$ locally cartesian closed?

**8**

**1**answer

### Example of a (presentable $k$-linear $\infty$-)category which is dualizable but not compactly generated?

**6**

**0**answers

### Double-categorical refinement of twisted arrow category: does it have a name?

**5**

**2**answers

### Does the Day convolution induce the structure of a bimonoidal category on $Fun(C,D)$?

**11**

**2**answers

### $(\infty,2)$-Categorical Analogue of the Local Nature of Equivalences

**15**

**1**answer

### A sheaf is a presheaf that preserves small limits

**4**

**1**answer

### Classes of monomorphisms - a definition

**3**

**1**answer

### When the global section functor is a Cartesian fibration?

**4**

**2**answers