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In the summer I will be teaching a course in (plane) Euclidean geometry to future high school teachers and I am looking for a suitable axiom system (unlike College (Euclidean) geometry textbook recommendations where books are discussed). Since the students should do a lot of ruler-and-compass constructions, I would like the axiom system to makeRead more

Hello, I know there are a lot of hosts who completely can’t stand these type of plug-ins and the hosts who offer accounts using them. I a… | Read the rest of http://www.webhostingtalk.com/showthread.php?t=1696370&goto=newpostRead more

I’m curious how much of homological algebra carries over to a constructive setting, like say HoTT (or some other variety of intensional type theory) without AC or excluded middle. There doesn’t seem to be a lot of literature on this topic (or at least it’s difficult for an outsider like me to find). The categoryRead more

I was reading the paper Towards Constructive Homological Algebra in Type Theory by Thierry Coquand and Arnaud Spiwack, and they state that constructively, the category of abelian groups fails to be abelian, because we cannot verify that every monic and epic map is normal. In particular, they say that given a monic map $ u:ARead more