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Formalization of diagram chasing as a first-order logic in Coq

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If you have a question about this talk, please contact Angeliki Koutsoukou-Argyraki.

Hybrid talk (please see abstract for link)

Diagram chasing is at the heart of many powerful tools in mathematics. Unfortunately, their usage requires a lot of tedious and technical calculations. For instance, one has to check the commutativity of many diagrams. These technicalities are often not detailed in papers, and can be a source of mistakes. This motivates the development of a formalized library to do diagram chasing on computer. In particular, a large part of the above mentioned computations can be automatized.

In this talk, after recalling the different notions, I will present the key points of such a library I am developing with Assia Mahboubi in Coq. In particular, I will explain that all the diagram chasing statements can be restated in a very simple language (in a first order logic), and I will state a formalized version of a often used duality meta-theorem.

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This talk is part of the Formalisation of mathematics with interactive theorem provers series.

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