https://media.ccc.de/c/qtcat2026 This feed contains all events from qtcat2026 as mp3 see video outro Wed, 12 Aug 2026 16:40:02 -0000 https://static.media.ccc.de/media/events/qtcat/2026/logo_light.png https://media.ccc.de/c/qtcat2026 https://media.ccc.de/v/qtcat-2026-110773-the-fundamental-theorem-of-deeper-algebra Higher algebra is the algebra of (connective) spectra. Deeper algebra is the algebra of (coconnective) categorical spectra. Deeper algebra organizes and simplifies many phenomena, from Galois theory to the classification of phases of matter. I will introduce these areas, and I will report on joint work in progress with David Reutter. Licensed to the public under https://creativecommons.org/licenses/by/4.0/ about this event: https://pretalx.c3voc.de/qtcat-2026/talk/9QMSKT/ Wed, 12 Aug 2026 14:00:00 +0200 https://cdn.media.ccc.de/events/qtcat/2026/mp3/qtcat2026-110773-eng-The_fundamental_theorem_of_deeper_algebra_mp3.mp3?1786549052 94cfe0a8-2a7d-58cc-9449-46949bc52126 2026-08-12T14:00:00+02:00 Theo Johnson-Freyd No 9QMSKT, 2026, qtcat2026, R. 221, qtcat2026-eng, Day 1 Higher algebra is the algebra of (connective) spectra. Deeper algebra is the algebra of (coconnective) categorical spectra. Deeper algebra organizes and simplifies many phenomena, from Galois theory to the classification of phases of matter. I will introduce these areas, and I will report on joint work in progress with David Reutter. Licensed to the public under https://creativecommons.org/licenses/by/4.0/ about this event: https://pretalx.c3voc.de/qtcat-2026/talk/9QMSKT/ 01:11:08 https://media.ccc.de/v/qtcat-2026-110760-who-cares-about-codensity-monads Consider the category of groups with its forgetful functor down to Set. This functor is monadic, which tells us that groups are sets equipped with an algebraic structure. Now consider the category of finite sets, with its inclusion into Set. This functor is not monadic for many reasons, but what monadic functor best approximates it? In other words, finite sets are most like sets equipped with what algebraic structure? The answer to this question is given my the codensity monad of FinSet -> Set. Quite surprisingly, this is the ultrafilter monad, whose algebras are compact Hausdorff spaces! That's all well an good, but why should you care? Every monad is trivially the codensity monad of some functor. Does it matter if it is the codensity monad of a specially nice one, say a fully faithful one? It does! For example, if a polynomial monad T on Set restricts to FinSet, then a general theory guarantees that there is a unique distributive law of the ultrafilter monad over T, i.e. a unique monad on CHaus which lifts T. In this talk I will tell you about this recent development about distributive laws involving codensity monads, and how they relate to the main subject of my thesis: pushforward monads. We will use the ulftrafilter monad as our central example. Licensed to the public under https://creativecommons.org/licenses/by/4.0/ about this event: https://pretalx.c3voc.de/qtcat-2026/talk/SBZJVC/ Wed, 12 Aug 2026 12:00:00 +0200 https://cdn.media.ccc.de/events/qtcat/2026/mp3/qtcat2026-110760-eng-Who_cares_about_codensity_monads_mp3.mp3?1786547095 25a00893-a118-5b86-8db3-85b06cbf1805 2026-08-12T12:00:00+02:00 Adrián Doña Mateo No SBZJVC, 2026, qtcat2026, R. 221, qtcat2026-eng, Day 1 Consider the category of groups with its forgetful functor down to Set. This functor is monadic, which tells us that groups are sets equipped with an algebraic structure. Now consider the category of finite sets, with its inclusion into Set. This functor is not monadic for many reasons, but what monadic functor best approximates it? In other words, finite sets are most like sets equipped with what algebraic structure? The answer to this question is given my the codensity monad of FinSet -> Set. Quite surprisingly, this is the ultrafilter monad, whose algebras are compact Hausdorff spaces! That's all well an good, but why should you care? Every monad is trivially the codensity monad of some functor. Does it matter if it is the codensity monad of a specially nice one, say a fully faithful one? It does! For example, if a polynomial monad T on Set restricts to FinSet, then a general theory guarantees that there is a unique distributive law of the ultrafilter monad over T, i.e. a unique monad on CHaus which lifts T. In this talk I will tell you about this recent development about distributive laws involving codensity monads, and how they relate to the main subject of my thesis: pushforward monads. We will use the ulftrafilter monad as our central example. Licensed to the public under https://creativecommons.org/licenses/by/4.0/ about this event: https://pretalx.c3voc.de/qtcat-2026/talk/SBZJVC/ 00:28:38 https://media.ccc.de/v/qtcat-2026-110765-the-road-from-circuits-to-category-theory String diagrams are often traced back to Richard Penrose's work in mathematical physics, but they also have an early and largely overlooked history in computer science through Günter Hotz. Following in the footsteps of Hotz, this talk will provide an introduction to string diagrams through the lens of circuit design. Rather than beginning with category theory, we start from circuits and their computational properties, and then work backwards to the categorical structures they describe. For example, we will see how modelling feedback motivates compact closed categories and reversibility suggests the structure of a monoidal dagger category. We will then see how the ability to copy data gives rise to Cartesian categories, with the no-cloning theorem identifying precisely why quantum circuits lack this structure. When circuits are no longer Cartesian, basic operations such as conditional statements become harder to reason about graphically. We conclude with a look at ongoing work on controlled monoidal categories and controlled string diagrams, which aim to restore graphical reasoning for conditional statements in non-Cartesian circuits. Licensed to the public under https://creativecommons.org/licenses/by/4.0/ about this event: https://pretalx.c3voc.de/qtcat-2026/talk/X8NKSX/ Wed, 12 Aug 2026 11:30:00 +0200 https://cdn.media.ccc.de/events/qtcat/2026/mp3/qtcat2026-110765-eng-The_Road_from_Circuits_to_Category_Theory_mp3.mp3?1786546897 2af093c5-e2e8-5299-a2e9-fb6d603d64c6 2026-08-12T11:30:00+02:00 Scott Wesley No X8NKSX, 2026, qtcat2026, R. 221, qtcat2026-eng, Day 1 String diagrams are often traced back to Richard Penrose's work in mathematical physics, but they also have an early and largely overlooked history in computer science through Günter Hotz. Following in the footsteps of Hotz, this talk will provide an introduction to string diagrams through the lens of circuit design. Rather than beginning with category theory, we start from circuits and their computational properties, and then work backwards to the categorical structures they describe. For example, we will see how modelling feedback motivates compact closed categories and reversibility suggests the structure of a monoidal dagger category. We will then see how the ability to copy data gives rise to Cartesian categories, with the no-cloning theorem identifying precisely why quantum circuits lack this structure. When circuits are no longer Cartesian, basic operations such as conditional statements become harder to reason about graphically. We conclude with a look at ongoing work on controlled monoidal categories and controlled string diagrams, which aim to restore graphical reasoning for conditional statements in non-Cartesian circuits. Licensed to the public under https://creativecommons.org/licenses/by/4.0/ about this event: https://pretalx.c3voc.de/qtcat-2026/talk/X8NKSX/ 00:34:09 https://media.ccc.de/v/qtcat-2026-110771-category-theory-formalised-humanely Formalisation is the process of expressing mathematical ideas in the language understood by a proof assistant, a computer program that enables the interactive construction of verified mathematical definitions, theorems, and proofs. The stereotypical understanding of formalisation is as the rote translation of pre-existing mathematics to a cumbersome formal language, done primarily as a means of certifying the correctness of an argument. This memetic conception as a chore standing in the way of a coveted result (guaranteed correctness) has long allowed the aesthetics of formalisation to be appropriated by adversarial actors to further their financial interests ("get paid for proving lemmas on the blockchain"/"our new LLM will totally solve All Of Maths, and we have the Lean to prove it"). I aim to challenge this understanding, presenting the process of formalisation, in itself, as a force for good. I will share some of my own experiences with free-and-libre, community-supported proof assistants as a tool for independent study; genuine mathematical insights revealed by developing category theory within formal univalent type theory; and a few challenges that come with maintaining a library of formalised mathematics. Licensed to the public under https://creativecommons.org/licenses/by/4.0/ about this event: https://pretalx.c3voc.de/qtcat-2026/talk/9F8KNH/ Wed, 12 Aug 2026 10:00:00 +0200 https://cdn.media.ccc.de/events/qtcat/2026/mp3/qtcat2026-110771-eng-Category_theory_formalised_humanely_mp3.mp3?1786546758 030bbd5a-36ca-58c3-847f-5c42016f0f27 2026-08-12T10:00:00+02:00 Amélia Liao No 9F8KNH, 2026, qtcat2026, R. 221, qtcat2026-eng, Day 1 Formalisation is the process of expressing mathematical ideas in the language understood by a proof assistant, a computer program that enables the interactive construction of verified mathematical definitions, theorems, and proofs. The stereotypical understanding of formalisation is as the rote translation of pre-existing mathematics to a cumbersome formal language, done primarily as a means of certifying the correctness of an argument. This memetic conception as a chore standing in the way of a coveted result (guaranteed correctness) has long allowed the aesthetics of formalisation to be appropriated by adversarial actors to further their financial interests ("get paid for proving lemmas on the blockchain"/"our new LLM will totally solve All Of Maths, and we have the Lean to prove it"). I aim to challenge this understanding, presenting the process of formalisation, in itself, as a force for good. I will share some of my own experiences with free-and-libre, community-supported proof assistants as a tool for independent study; genuine mathematical insights revealed by developing category theory within formal univalent type theory; and a few challenges that come with maintaining a library of formalised mathematics. Licensed to the public under https://creativecommons.org/licenses/by/4.0/ about this event: https://pretalx.c3voc.de/qtcat-2026/talk/9F8KNH/ 01:04:02 https://media.ccc.de/v/qtcat-2026-110775-opening Opening of QTCat! Licensed to the public under https://creativecommons.org/licenses/by/4.0/ about this event: https://pretalx.c3voc.de/qtcat-2026/talk/G8V7E7/ Wed, 12 Aug 2026 09:45:00 +0200 https://cdn.media.ccc.de/events/qtcat/2026/mp3/qtcat2026-110775-eng-Opening_mp3.mp3?1786541342 41953ecd-0a67-58e4-a9e0-d409daab9640 2026-08-12T09:45:00+02:00 Tessa Kammermeier No G8V7E7, 2026, qtcat2026, R. 221, qtcat2026-eng, Day 1 Opening of QTCat! Licensed to the public under https://creativecommons.org/licenses/by/4.0/ about this event: https://pretalx.c3voc.de/qtcat-2026/talk/G8V7E7/ 00:04:01 media.ccc.de / RSS 0.3.3 CCC media team media@c3voc.de CCC media team No CCC Congress Hacking Security Netzpolitik A wide variety of video material distributed by the CCC. 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