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"url": "https://bartoszmilewski.com/2019/07/03/programming-with-universal-constructions/", "published_at": "2019-07-03T16:39:55+00:00" }, { "id": "01a0e480-d8a0-7255-a43d-766bc4a9ee60", "title": "Promonads, Arrows, and Einstein Notation for Profunctors", "url": "https://bartoszmilewski.com/2019/03/27/promonads-arrows-and-einstein-notation-for-profunctors/", "published_at": "2019-03-27T18:34:21+00:00" }, { "id": "01a0e480-d8a0-7255-a43d-766bc4a9f179", "title": "ACT2019 School: Call for Participation", "url": "https://bartoszmilewski.com/2019/01/05/act2019-school-call-for-participation/", "published_at": "2019-01-06T06:49:52+00:00" }, { "id": "01a0e480-d8a0-7255-a43d-766bc53c096c", "title": "Metamorphisms", "url": "https://bartoszmilewski.com/2019/01/03/metamorphisms/", "published_at": "2019-01-03T19:26:09+00:00" }, { "id": "01a0e480-d8a0-7255-a43d-766bc624a396", "title": "Open Season on Hylomorphisms", "url": "https://bartoszmilewski.com/2018/12/20/open-season-on-hylomorphisms/", "published_at": "2018-12-20T20:35:54+00:00" }, { "id": "01a0e480-d8a0-7255-a43d-766bc6f84796", "title": "Keep it Simplex, Stupid!", "url": "https://bartoszmilewski.com/2018/12/11/keep-it-simplex-stupid/", "published_at": "2018-12-11T20:10:58+00:00" }, { "id": "01a0e480-d8a0-7255-a43d-766bc7b8c291", "title": "Trading FunLists at a Bazaar with Yoneda", "url": "https://bartoszmilewski.com/2018/10/12/trading-funlists-at-a-bazaar-with-yoneda/", "published_at": "2018-10-12T20:44:29+00:00" }, { "id": "01a0e480-d8a0-7255-a43d-766bc886b9e2", "title": "Recursion Schemes for Higher Algebras", "url": "https://bartoszmilewski.com/2018/08/20/recursion-schemes-for-higher-algebras/", "published_at": "2018-08-20T17:09:38+00:00" }, { "id": "01a0e480-d8a0-7255-a43d-766bc8b0ebfd", "title": "Free Monoid from Free Algebra, Part 2", "url": "https://bartoszmilewski.com/2018/07/30/free-monoid-from-free-algebra-part-2/", "published_at": "2018-07-31T02:58:38+00:00" }, { "id": "01a0e490-596c-715e-86a5-b1afa368655c", "title": "Free Monoid from Free Algebra, Part 1", "url": "https://bartoszmilewski.com/2018/07/30/free-monoid-from-free-algebra-part-1/", "published_at": "2018-07-31T02:46:20+00:00" }, { "id": "01a0e490-596c-715e-86a5-b1afa3a1085f", "title": "Free Monoidal Functors, Categorically!", "url": "https://bartoszmilewski.com/2018/05/16/free-monoidal-functors-categorically/", "published_at": "2018-05-16T21:00:54+00:00" }, { "id": "01a0e490-596c-715e-86a5-b1afa4597167", "title": "Life and (Thermal) Death in the Universe", "url": "https://bartoszmilewski.com/2018/03/28/life-and-thermal-death-in-the-universe/", "published_at": "2018-03-28T17:23:58+00:00" }, { "id": "01a0e490-596c-715e-86a5-b1afa475d2b4", "title": "Free Monoidal Profunctors", "url": "https://bartoszmilewski.com/2018/02/20/free-monoidal-profunctors/", "published_at": "2018-02-20T15:48:37+00:00" }, { "id": "01a0e490-596c-715e-86a5-b1afa568bf81", "title": "Free Monoidal Functors", "url": "https://bartoszmilewski.com/2018/02/17/free-monoidal-functors/", "published_at": "2018-02-17T17:21:46+00:00" }, { "id": "01a0e490-596c-715e-86a5-b1afa64ed9bc", "title": "Pointwise Kan Extensions", "url": "https://bartoszmilewski.com/2018/01/23/pointwise-kan-extensions/", "published_at": "2018-01-23T12:20:25+00:00" }, { "id": "01a0e490-596c-715e-86a5-b1afa7184d9e", "title": "The Earth is Flat", "url": "https://bartoszmilewski.com/2018/01/11/the-earth-is-flat/", "published_at": "2018-01-11T14:00:41+00:00" }, { "id": "01a0e490-596c-715e-86a5-b1afa7948b67", "title": "Stalking a Hylomorphism in the Wild", "url": "https://bartoszmilewski.com/2017/12/29/stalking-a-hylomorphism-in-the-wild/", "published_at": "2017-12-29T21:46:38+00:00" }, { "id": "01a0e490-596c-715e-86a5-b1afa847ea03", "title": "Monads, Monoids, and Categories", "url": "https://bartoszmilewski.com/2017/09/06/monads-monoids-and-categories/", "published_at": "2017-09-07T06:07:35+00:00" }, { "id": "01a0e490-596c-715e-86a5-b1afa8caebb6", "title": "Lawvere Theories", "url": "https://bartoszmilewski.com/2017/08/26/lawvere-theories/", "published_at": "2017-08-26T18:28:51+00:00" }, { "id": "01a0e4a2-8792-7222-ab68-c7b2f9efa26a", "title": "Topoi", "url": "https://bartoszmilewski.com/2017/07/22/topoi/", "published_at": "2017-07-22T17:15:03+00:00" }, { "id": "01a0e4a2-8792-7222-ab68-c7b2fa74b983", "title": "Profunctor Optics: The Categorical View", "url": "https://bartoszmilewski.com/2017/07/07/profunctor-optics-the-categorical-view/", "published_at": "2017-07-07T21:08:52+00:00" }, { "id": "01a0e4a2-8792-7222-ab68-c7b2fb13dadd", "title": "Enriched Categories", "url": "https://bartoszmilewski.com/2017/05/13/enriched-categories/", "published_at": "2017-05-13T12:15:01+00:00" }, { "id": "01a0e4a2-8792-7222-ab68-c7b2fbfdc2ff", "title": "Kan Extensions", "url": "https://bartoszmilewski.com/2017/04/17/kan-extensions/", "published_at": "2017-04-17T16:09:49+00:00" }, { "id": "01a0e4a2-8792-7222-ab68-c7b2fc842b71", "title": "Profunctor Parametricity", "url": "https://bartoszmilewski.com/2017/04/11/profunctor-parametricity/", "published_at": "2017-04-11T20:59:18+00:00" }, { "id": "01a0e4a2-8792-7222-ab68-c7b2fd10d269", "title": "Ends and Coends", "url": "https://bartoszmilewski.com/2017/03/29/ends-and-coends/", "published_at": "2017-03-29T16:30:12+00:00" }, { "id": "01a0e4a2-8792-7222-ab68-c7b2fd278728", "title": "Algebras for Monads", "url": "https://bartoszmilewski.com/2017/03/14/algebras-for-monads/", "published_at": "2017-03-14T21:06:52+00:00" }, { "id": "01a0e4a2-8792-7222-ab68-c7b2fd87c674", "title": "F-Algebras", "url": "https://bartoszmilewski.com/2017/02/28/f-algebras/", "published_at": "2017-02-28T19:43:05+00:00" }, { "id": "01a0e4a2-8792-7222-ab68-c7b2fe65e923", "title": "Monoids on Steroids", "url": "https://bartoszmilewski.com/2017/02/09/monoids-on-steroids/", "published_at": "2017-02-09T20:20:02+00:00" }, { "id": "01a0e4a2-8792-7222-ab68-c7b2feda191e", "title": "Applicative Functors", "url": "https://bartoszmilewski.com/2017/02/06/applicative-functors/", "published_at": "2017-02-06T17:45:34+00:00" } ] posts Claim your blog

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Bartosz Milewski

bartoszmilewski.com

2026

Tannakian Reconstruction in a Yoneda Equipment original ↗

21 Sept 2026

Yoneda Lemma in Double Categories original ↗

13 Sept 2026

Profunctor Optics original ↗

19 Jul 2026

Tannakian reconstruction original ↗

14 Jul 2026

Tambara Equipment original ↗

11 Jul 2026

Actegories original ↗

30 Jun 2026

Kan Extensions in Double Categories original ↗

13 Jun 2026

Kan Extensions in Haskell original ↗

8 Jun 2026

Tabulation Tribulations original ↗

23 May 2026

Bending, Yanking, and Cartesian Squares in Double Categories original ↗

19 May 2026

Profunctor Equipment in Haskell original ↗

16 May 2026

Profunctor Equipment original ↗

24 Apr 2026

The Axiom of Univalence original ↗

10 Mar 2026

2025

Modeling Identity Types original ↗

18 Oct 2025

Identity Types original ↗

22 Sept 2025

Models of (Dependent) Type Theory original ↗

5 Sept 2025

(Weak) Factorization Systems original ↗

26 Jul 2025

(Weak) Homotopy Equivalences original ↗

20 Jun 2025

Fibrations and Cofibrations original ↗

30 May 2025

Subfunctor Classifier original ↗

21 Apr 2025

Subobject Classifier original ↗

20 Mar 2025

Linklog | Understanding Attention in LLMs original ↗

7 Mar 2025

Legalizing Comonad Composition original ↗

4 Jan 2025

2024

Sieves and Sheaves original ↗

16 Nov 2024

Covering Sieves original ↗

31 Oct 2024

Sheaves as Virtual Objects original ↗

24 Oct 2024

Coverages and Sites original ↗

7 Oct 2024

Sheaves and Topology original ↗

18 Aug 2024

Presheaves and Topology original ↗

7 Aug 2024

Topology as a Dietary Choice original ↗

12 Jul 2024

Neural Networks, Pre-lenses, and Triple Tambara Modules, Part II original ↗

24 Mar 2024

Neural Networks, Pre-Lenses, and Triple Tambara Modules original ↗

22 Mar 2024

Linear Lenses in Haskell original ↗

7 Feb 2024

2023

Exercise in Coherence original ↗

19 Sept 2023

2022

Teaching optics through conspiracy theories original ↗

5 Apr 2022

2021

Co-Presheaf Optics original ↗

29 Dec 2021

Symmetries and Redundancies original ↗

20 Dec 2021

Profunctor Representation of a Polynomial Lens original ↗

10 Dec 2021

Polynomial Lens in Idris original ↗

9 Dec 2021

PolyLens original ↗

7 Dec 2021

Actegories and Lenses original ↗

5 Dec 2021

Optics for the Working Mathematician original ↗

8 Sept 2021

Dependent Optics original ↗

4 Sept 2021

Traversals 3: Existential and Profunctor representations of Traversals original ↗

1 Apr 2021

Traversals 2: Profunctors and Tambara Modules original ↗

1 Apr 2021

Traversals 1: van Laarhoven and Existentials original ↗

1 Apr 2021

Functorio original ↗

16 Feb 2021

2020

The Fall of the SKI Civilization original ↗

6 Sept 2020

Benign Data Races Considered Harmful original ↗

11 Aug 2020

Categories for the Working C++ Programmer original ↗

5 Aug 2020

Defunctionalization and Freyd’s Theorem original ↗

3 Aug 2020

Freyd’s Adjoint Functor Theorem original ↗

22 Jul 2020

Weighted Colimits original ↗

20 Jul 2020

Monoidal Catamorphisms original ↗

15 Jun 2020

Guitar Decomposed: 9. Extension Chords original ↗

11 Jun 2020

Guitar Decomposed: 8. Ninth Chords original ↗

2 Jun 2020

Guitar Decomposed: 7. Major Seventh Chords original ↗

30 May 2020

Guitar Decomposed: 6. Dominant Seventh Chords original ↗

28 May 2020

Guitar Decomposed: 5. Mutating the Third original ↗

28 May 2020

Guitar Decomposed: 4. The Grand Unification original ↗

27 May 2020

Guitar Decomposed: 3. Moving Sideways original ↗

26 May 2020

Guitar Decomposed: 2. Moving Up original ↗

25 May 2020

Guitar Decomposed: 1. Weird Logic Behind Tuning original ↗

24 May 2020

On Composability original ↗

22 May 2020

Terminal Coalgebra as Directed Limit original ↗

22 Apr 2020

Initial Algebra as Directed Colimit original ↗

10 Apr 2020

Math is your insurance policy original ↗

24 Feb 2020

2019

Fixed Points and Diagonal Arguments original ↗

7 Nov 2019

Fibrations, Cleavages, and Lenses original ↗

10 Oct 2019

The Power of Adjunctions original ↗

20 Sept 2019

Filtered Colimits original ↗

4 Jul 2019

Programming with Universal Constructions original ↗

3 Jul 2019

Promonads, Arrows, and Einstein Notation for Profunctors original ↗

27 Mar 2019

ACT2019 School: Call for Participation original ↗

6 Jan 2019

Metamorphisms original ↗

3 Jan 2019

2018

Open Season on Hylomorphisms original ↗

20 Dec 2018

Keep it Simplex, Stupid!original ↗

11 Dec 2018

Trading FunLists at a Bazaar with Yoneda original ↗

12 Oct 2018

Recursion Schemes for Higher Algebras original ↗

20 Aug 2018

Free Monoid from Free Algebra, Part 2 original ↗

31 Jul 2018

Free Monoid from Free Algebra, Part 1 original ↗

31 Jul 2018

Free Monoidal Functors, Categorically!original ↗

16 May 2018

Life and (Thermal) Death in the Universe original ↗

28 Mar 2018

Free Monoidal Profunctors original ↗

20 Feb 2018

Free Monoidal Functors original ↗

17 Feb 2018

Pointwise Kan Extensions original ↗

23 Jan 2018

The Earth is Flat original ↗

11 Jan 2018

2017

Stalking a Hylomorphism in the Wild original ↗

29 Dec 2017

Monads, Monoids, and Categories original ↗

7 Sept 2017

Lawvere Theories original ↗

26 Aug 2017

Topoi original ↗

22 Jul 2017

Profunctor Optics: The Categorical View original ↗

7 Jul 2017

Enriched Categories original ↗

13 May 2017

Kan Extensions original ↗

17 Apr 2017

Profunctor Parametricity original ↗

11 Apr 2017

Ends and Coends original ↗

29 Mar 2017

Algebras for Monads original ↗

14 Mar 2017

F-Algebras original ↗

28 Feb 2017

Monoids on Steroids original ↗

9 Feb 2017

Applicative Functors original ↗

6 Feb 2017