CSCAT 2021

理論計算機科学と圏論ワークショップ

Computer Science and Category Theory

日時：2021年3月18日（木）〜2021年3月19日（金）

Date: 18 (Thu) -- 19 (Fri) March 2021

オンライン(zoom)での開催です。

CSCAT 2021 will be held online (zoom).

幹事：星野直彦（崇城大学、hnaohiko@gmail.com)

Organizer: Naohiko Hoshino (Sojo university)

email: hnaohiko@gmail.com

CSCATとは

CSCAT（理論計算機科学と圏論ワークショップ）は、数学の分野である圏論の情報科学への応用に関心を持つ研究者による研究集会です。通常の学会では、時間の制約などのため研究の詳細にまで立ち入った発表と議論はなかなかむずかしいのが実情です。本研究集会は、１つ１つの発表に長い時間を割り当て、じっくりと話を聞き議論する場を提供することを目的としています。

参加登録 （3月16日締切）

発表の有無に関わらず、CSCAT参加登録（google form）からお願いします。回答の変更などは星野（hnaohiko@gmail.com）にお送りください。

Registration (Please register before 16 March)

Click here (google form) to register.

Program

3/18

13:00 - 13:20 諸連絡

13:20 - 14:00 郡茉友子 "Initial Algebra-Final Coalgebra Coincidence in Fibrations"

14:00 - 14:40 眞田嵩大 "Category-Graded Algebraic Theories and Effect Handlers"

14:40 - 15:00 休憩

15:00 - 15:40 藤井宗一郎 "Completeness and injectivity"

15:40 - 16:20 山本雄太 "鎖複体の型理論"

3/19

13:20 - 14:00 前原 悠究 "Orientals as free weak ω-categories"

14:00 - 14:40 浦本武雄 "Witt vectors over imaginary quadratic fields from Fricke functions"

14:40 - 15:00 休憩

15:00 - 15:40 中田哲 "Parallelism in realizability models"

15:40 - 16:20 吹原耀司 "Generalization of Bounded Linear Logic and its Categorical Semantics"

16:20 - 16:30 クロージング

Title and abstract

  • 藤井宗一郎 / Soichiro Fujii （京都大）

Title: Completeness and injectivity

Abstract: We show that for any quantale Q, a Q-category is skeletal and complete if and only if it is injective with respect to fully faithful Q-functors. This is a special case of known theorems due to Hofmann and Stubbe, but we provide a different proof, using the characterisation of the MacNeille completion of a Q-category as its injective envelope.


  • 郡茉友子/Mayuko Kori（総研大）

Title: Initial Algebra-Final Coalgebra Coincidence in Fibrations

Abstract: TBA


  • 中田哲/Satoshi Nakata （京都大）

Title: Parallelism in realizability models


Abstract: In this talk, by abstracting Plotkin's parallel-or function, we define the notions of parallel-or and parallel-and in an arbitrary Partial Combinatory Algebra (PCA). We then consider how the structure of realizability models is affected by the parallel operations. For example, these are related to a “restricted subobject classifier” (called predominance; it is introduced by Rosolini) in the category Ass(A) of assemblies over PCA A. Under a natural assumption on a predominance t in Ass(A), we show that t is a dominance if and only if A admits a parallel-and combinator for t.


  • 前原 悠究/Yuki Maehara（九州大）

Title: Orientals as free weak ω-categories

Abstract: The orientals were introduced by Street as the free strict ω-categories on the simplices, and they play a fundamental role in the simplicial approach to higher-dimensional category theory. The main result of this work is that these orientals are also the free weak ω-categories on the same generating data. I will devote most of the talk to explaining the motivation and the intuition behind relevant notions.

  • 山本雄太/Yamamoto Yuta（東京大）

Title: 鎖複体の型理論

Abstract: 鎖複体をモデルに持つような型理論を構築する。これによりホモロジー代数についてのsyntheticな推論ができるようになるだけでなく、path typeを糖衣構文として定義することのできるnull typeという新しい型構成子を発見した。

  • 眞田嵩大/Takahiro Sanada（京都大）

Title: Category-Graded Algebraic Theories and Effect Handlers

Abstract: We provide an effect system CatEff based on a category-graded extension of algebraic theories that correspond to category-graded monads. Our effect system has category-graded operations and handlers. Effects are graded by morphisms of the grading category. Grading morphisms represent fine structures of effects such as dependencies or sorts of states. Category-graded handlers are regarded as an implementation of category-graded effects. We give an example using category-graded effects to represent computational effect such as sending and receiving typed data.

  • 浦本武雄/Takeo Uramoto（九州大）

Title: Witt vectors over imaginary quadratic fields from Fricke functions

Abstract: In this talk I introduce an application of the formal theory of semi-galois categories (= monoid extension of galois categories, originated in automata theory) to a certain arithmetic problem concerning analytic construction of generalized Witt vectors. In my former talk at ALGI2020, I introduced that algebraic Witt vectors over imaginary quadratic fields can be obtained by special values of certain deformation families of modular functions. Later, after several confusions, I noticed more satisfactory proofs for stronger results, showing that algebraic Witt vectors over any imaginary quadratic field are precisely those obtained from deformations of certain specific modular functions called Fricke functions. My emphasis in this talk will be put on the fact that several categorical concepts (say galois objects, duality) in the formal theory of semi-galois categories play key roles in my proofs and show some notable harmony with several classical arithmetic concepts such as modular functions and complex multiplication. If time allows, I may also discuss some function-field analogue of these arithmetic results.

  • 吹原耀司/Yoji Fukihara（京都大）

Title: Generalization of Bounded Linear Logic and its Categorical Semantics

Abstract: We introduce a generalization of Girard et al.'s BLL called GBLL (and its affine variant GBAL). It is designed to capture the core mechanism of dependency in BLL, while it is also able to separate complexity aspects of BLL. We analyze the complexity of cut-elimination in GBLL, and give a translation from BLL with constraints to GBAL with positivity axiom. We then introduce indexed linear exponential comonads (ILEC for short) as a categorical structure for interpreting the !-modality of GBLL. By using the category of assemblies, we obtain a 'index-dependent' realizability semantics of BLL.

過去の CSCAT