Towards a Readable Formalisation of Category Theory
نویسنده
چکیده
We formally develop category theory up to Yoneda’s lemma, using Isabelle/HOL/Isar, and survey previous formalisations. By using recently added Isabelle features, we have produced a formal text that more closely approximates informal mathematics.
منابع مشابه
TOWARDS THE THEORY OF L-BORNOLOGICAL SPACES
The concept of an $L$-bornology is introduced and the theory of $L$-bornological spacesis being developed. In particular the lattice of all $L$-bornologies on a given set is studied and basic properties ofthe category of $L$-bornological spaces and bounded mappings are investigated.
متن کاملA Category-Theoretic Approach to Social Network Analysis
In this paper we introduce a category-theoretic formalisation of social network analysis. This generalises traditional graph-theoretic formalisations and facilitates a formal approach to statements and beliefs about social networks. We describe a formal semantics for belief in social networks, and we illustrate our formalisation by a case study drawn from organisational structure in the Gulf War.
متن کاملWild ω-Categories for the Homotopy Hypothesis in Type Theory
In classical homotopy theory, the homotopy hypothesis asserts that the fundamental ω-groupoid construction induces an equivalence between topological spaces and weak ω-groupoids. In the light of Voevodsky’s univalent foundations program, which puts forward an interpretation of types as topological spaces, we consider the question of transposing the homotopy hypothesis to type theory. Indeed suc...
متن کاملA Syntactic Proof of Arrow's Theorem in a Modal Logic of Social Choice Functions
We show how to formalise Arrow’s Theorem on the impossibility of devising a method for preference aggregation that is both independent of irrelevant alternatives and Pareto efficient by using a modal logic of social choice functions. We also provide a syntactic proof of the theorem in that logic. While prior work has been successful in applying tools from logic and automated reasoning to social...
متن کاملRe-reading the Narrative in Ibrahim Sultan’s Shahnama Based on Paul Ricoeur`s Philosophical Hermeneutics Theory
A manuscript of Ibrahim Sultan`s Shahnama available at the Bodleian Library of Oxford, representing the full range of visual features of the Shiraz School at the age of Ibrahim Sultan Timuri (817-838 AH) which has the symbolic aspects and semantic trends of painting and the potentiality to be interpreted based on philosophical hermeneutics. It seems that analyzing the visual element and re...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Electr. Notes Theor. Comput. Sci.
دوره 91 شماره
صفحات -
تاریخ انتشار 2004