Tag: adjoint-functors

74 How do I check if a functor has a (left/right) adjoint? 2009-11-17T06:21:13.817

50 What is an intuitive view of adjoints? (version 1: category theory) 2009-11-23T09:31:28.447

32 Does a scheme have a "separification"? 2009-10-13T04:16:20.170

32 Is there an explicit construction of a free coalgebra? 2010-07-08T20:09:15.997

31 Properties of functors and their adjoints 2012-06-27T21:19:54.220

23 Are there non-trivial infinite chains of adjoint functors? 2016-06-16T14:18:53.450

22 Is every functor a composition of adjoint functors? 2009-10-12T03:51:02.110

21 When and why do universal objects have extra properties? 2009-11-24T17:43:06.650

19 Does the forgetful functor {Hopf Algebras}→{Algebras} have a right adjoint? 2010-04-27T00:47:43.993

17 Can adjoint linear transformations be naturally realized as adjoint functors? 2009-10-14T03:18:35.247

16 What's an example of an "adjunction up to adjunction"? 2009-10-28T18:58:18.720

16 Lurie's approach to the bar-cobar adjunction 2014-12-17T23:03:19.980

16 If a right adjoint to the product functor exists, must it be the diagonal? 2017-04-13T06:43:32.157

13 Is there a monad on Set whose algebras are Tychonoff spaces? 2013-06-28T15:03:11.473

12 Is a functor which has a left adjoint which is also its right adjoint an equivalence ? 2009-12-05T22:27:50.633

12 Iterated adjoint functors 2009-12-27T04:06:24.920

12 Fullness of pullback functor in algebraic geometry 2012-07-12T18:38:50.287

12 Verifying that $\epsilon^!$ is indeed the right adjoint of $\epsilon_*$ in the context of algebraic stacks 2015-05-20T05:16:53.073

11 Can different modules have the same symmetric algebra? (answered: no) 2009-11-23T08:21:33.067

11 Is every saft category cocomplete? 2010-12-12T21:17:53.357

10 When does the sheaf direct image functor f_* have a right adjoint? 2009-10-27T19:58:07.950

10 Adjoint Functors as Initial Objects of Some Category 2012-11-25T03:04:36.950

10 On the coherence theorem for bicategories 2015-03-02T13:19:05.203

10 Categories which are both monadic and comonadic over another category 2017-06-26T11:20:53.163

9 An elementary question about adjunctions between presheaf categories preserving pullbacks. 2010-08-03T20:07:25.923

9 The category of categories and adjunctions 2014-08-08T20:57:29.507

8 Left adjoint pseudofunctor commutes with pseudocolimits 2017-11-06T23:41:18.833

8 "Equivalence" is to "group" as "adjoint" is to ....? 2017-12-21T15:16:15.820

7 Is there a free digraph associated to a graph? 2009-10-21T10:11:23.650

7 [Reference Request] The Definition of Adjoint Functors between dg-categories 2012-09-23T05:52:45.807

7 Is every functor inducing a homotopy equivalence a composition of adjoint functors? 2012-12-28T11:36:14.523

7 Constructing pointwise Kan extensions as adjoints to some functor 2013-03-18T02:27:29.847

7 bar-cobar or cobar-bar 2013-04-02T19:42:40.807

7 How to construct a free 2-group on a groupoid? 2014-07-10T11:09:10.960

6 Proving the Special Adjoint Functor Theorem from the general Adjoint Functor Theorem 2010-05-24T19:19:39.277

6 Cofree Lie Coalgebra 2014-11-16T18:05:46.713

6 Exactness of an additive left Kan extension 2014-11-24T17:47:55.897

5 Kan extensions and the yoneda embedding. 2010-05-06T22:33:06.227

5 Not quite adjoint functors 2014-02-11T21:23:31.717

5 Map of adjunctions 2014-12-03T01:37:36.707

5 Uniqueness of $\infty$-adjoints 2016-02-22T22:41:42.327

5 Finite well-completeness and the small object argument? 2016-08-04T21:22:57.847

5 About small $\omega$-orthogonality classes and Gabriel-Ulmer duality 2017-07-24T16:40:54.697

4 "adjoint" =?= "inverse of composite endofunctor is uniform bi-composition" 2010-03-23T20:08:47.880

4 Free monad or monad defined from an adjunction. 2010-05-22T16:22:19.633

4 Adjunctions: Algebras of the induced monad VS. Coalgebras of the induced comonad. 2010-08-26T14:00:39.307

4 On the barycentric subdivision of a poset 2011-03-07T15:43:48.350

4 A Question on Auto-Adjoint functors 2012-09-02T21:18:41.363

4 Do generalizations of adjoint functors, such as adjunctions in 2-categories, and multivariable adjunctions, have formulations in terms of something like universal morphisms? 2013-03-18T00:12:31.663

4 When are induction and coinduction of representations of Lie groups isomorphic? When they are compact? Semisimple? 2014-09-10T13:49:20.533

4 Left adjoint of pullback 2015-11-22T00:09:50.837

4 Does the inclusion of presheaves into families of sets have a left adjoint? 2016-06-29T04:37:04.067

4 Left adjoint for categories of commutative monoids? 2016-08-26T16:22:07.340

4 Left adjoint to inclusion of Connected Groupoids into Groupoids 2016-11-06T14:52:53.587

4 Free functors having a left adjoint 2017-01-10T18:27:13.267

4 About small-orthogonality classes of a locally presentable category 2017-07-14T15:55:51.363

3 What is the "right" definition of the free abelian group on a set? 2009-11-22T23:04:51.030

3 a “self-dual” adjunction 2011-07-14T18:13:37.067

3 Adjunctions between derived functors 2011-11-29T20:15:18.837

3 Why is $Lex(\mathcal{A},\mathcal{Ab})$ abelian? Does $Lex(\mathcal{A},\mathcal{Ab})\rightarrow Func(\mathcal{A},\mathcal{Ab})$ admit a left-adjoint? 2013-05-11T14:25:14.637

3 Categories where morphisms are pairs of adjoint functors 2013-07-23T09:29:11.440

3 Functoriality of the adjoint functor construction? 2014-11-26T23:05:37.880

3 Question about Enriched Categories and Functors 2015-12-29T03:36:45.557

3 What do you get when you apply a universal cocone to a colimit functor 2015-12-30T21:08:56.917

3 "2-Sheafification" with Values in non $Cat$ categories? 2016-07-31T03:52:03.290

3 Why quasi-inverse functors are adjoint pairs? 2016-11-03T03:46:19.007

3 Is there a construction capturing indexed families of adjunctions? 2016-12-05T15:43:05.843

3 Fundamental monoid pertaining to adjunctions 2017-04-03T15:08:52.600

3 Translating parabolic induction as $\Lambda G^F/U^F\otimes_{\Lambda L^F}-$ to $\hom_{\Lambda L^F}(\Lambda U^F/G^F,-)$? 2017-09-19T07:32:59.543

3 Can the cobordism hypothesis be formulated as a statement about adjoint functors? 2017-12-13T11:32:43.107

2 How to construct pair of adjoint functors from category A to category A_D(category of diagrams) 2009-11-25T08:08:59.167

2 Left adjoint Grp->Set?? 2010-02-27T14:18:22.860

2 How is the right adjoint $f_*$ to the inverse image functor $f^*$ described for functor categories $Set^C$, $Set^D$ and $f : C \to D$ 2010-07-21T11:40:57.483

2 Reference request: 2-Monads and 2-Adjunctions 2011-01-23T20:14:33.227

2 Is there an analog of adjoint functor theorem for adjunctions of two variables? 2013-03-21T10:02:28.207

2 admissible subcategories over non algebraically closed fields 2013-05-27T20:18:56.330

2 A Criterion for a morphism to be a counit of an Adjunction 2014-01-27T21:23:17.103

2 Simple technical adjunction question 2014-04-01T20:49:32.757

2 Are the pullback functors of adjoint functors also adjoint? 2014-08-14T13:23:05.377

2 Notions of/References for freely generated (symmetric) monoidal categories 2015-03-24T17:51:13.387

2 Free commutative monoid monad 2016-10-29T22:28:14.083

2 Intrinsic notions of étale? 2016-12-05T12:26:47.403

2 Right adjoint completions 2017-08-27T22:34:59.293

2 Adjoints for the functor ${\bf Top}\to {\bf Conv}$ 2017-10-13T07:03:09.583

2 On the History of Double Adjoints 2017-11-30T15:26:33.963

1 Does every cocontinuous functor between categories of presheaves on small categories have a right adjoint? 2010-04-14T16:59:41.063

1 Relating eigenvectors of two self-adjoints operators 2011-10-26T13:02:32.933

1 Can we characterize endofunctors which admit a monad structure? 2013-01-13T20:47:57.663

1 Another adjoint pair: Definable sets and set-builder formulas 2013-10-29T16:28:17.147

1 Category which has no non-trivial adjoint functors 2014-08-09T16:10:31.307

1 Faithfulness of Right adjoint to Kan extension 2016-12-26T03:09:02.960

1 link between completion of the universal enveloping algebra and an endomorphism of functor 2017-03-01T13:51:06.397

0 Basic category theory: Universality of adjunction unit is justified by Yoneda Proposition in Mac Lane's text 2014-07-02T16:15:38.737

0 Adjointable Abelian Monoidal Functor 2015-07-29T18:32:12.437

0 Four questions about C12 generators and adjunction 2016-09-01T15:36:29.440

0 Is "square" functor monomorphic on objects? 2017-10-16T20:40:08.047

-1 irreducible Classical Lie algebras 2013-11-06T22:56:27.883

-1 General description of transition arrows of covering morphisms in family fibrations 2017-01-02T21:01:22.840