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### bar-cobar or cobar-bar

What is the standard or best reference for the adjointnes of bar and cobar constructions?

**6**

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815 views

### Proving the Special Adjoint Functor Theorem from the general Adjoint Functor Theorem

Often, when dealing with adjoint functor theorems, people go about proving each one separately, from first principles if you will (this is the course taken in MacLane). However, the names suggest ...

**5**

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69 views

### Uniqueness of lax 2-adjoints

In this nlab page there is defined the notion of a lax 2-adjoint. My question is to what extent would an adjoint of this type be unique?

**5**

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415 views

### Constructing pointwise Kan extensions as adjoints to some functor

Background
I'm working on formalizing some category theory in Coq at https://bitbucket.org/JasonGross/catdb. Currently, I'm in the process of formalizing pointwise Kan extensions. Partly because I'...

**4**

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113 views

### Cofree Lie Coalgebra

I have problems finding anything about the cofree Lie coalgebra functor
$\mathcal{L}ie^c$ out there.
Basically all I found was that it appears in Harrison cohomology and that,
given a $\mathbb{Z}$-...

**3**

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182 views

### Map of adjunctions

The following question must have been asked dozens of times, but I do not recall any non-trivial results.
Consider an adjoint square where the arrows indicate directions of $F, G, H, K$.
$\require{...

**3**

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242 views

### Do generalizations of adjoint functors, such as adjunctions in 2-categories, and multivariable adjunctions, have formulations in terms of something like universal morphisms?

I recently learned about two-variable adjunctions and multi-variable adjunctions, and about adjunctions in 2-categories. The nCatLab page on two-variable adjunctions talks about how to go from the ...

**2**

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81 views

### Notions of/References for freely generated (symmetric) monoidal categories

We often describe a category by giving a (directed, multi-)graph and freely generating a category of paths. I would like to know to what degree this intuition generalizes to monoidal categories, and ...