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2
votes
2answers
625 views

Constructing dependent product (right adjoint to pullback) in a locally cartesian closed category

I've been trying to find a proof that the pullback functors in a locally cartesian closed category have right adjoints (used to model the notion of indexed product inside a category (rather than ...
3
votes
2answers
100 views

Is there a (foundational) type theory with the features I'm looking for?

I like to distinguish between sets and subsets. We imagine that sets are floating free in the universe, and that the elements of a set are constructed according to some kind of recursive rules. Like ...
41
votes
6answers
5k views

Learning Lambda Calculus

What are some good online/free resources (tutorials, guides, exercises, and the like) for learning Lambda Calculus? Specifically, I am interested in the following areas: Untyped lambda calculus ...
15
votes
3answers
598 views

What good is infinity?

I am becoming increasingly convinced that Wildberger's views are, if a little bizarre, at least not hopelessly inconsistent. When I was reading the comments in the video following (MF17), somebody ...
2
votes
2answers
101 views

Variables in Types in type theory

I'm slowly grasping this, though the different formulations of type theory make it difficult. In http://imps.mcmaster.ca/doc/seven-virtues.pdf types can only be formed from *, i, and a->b when a and ...
0
votes
1answer
216 views

How to understand inductive definitions of recursive data types?

The problem was encountered when learning Computability Notes by Roberto Zunino (link), page 9 and 11. It seems as if it is a well-known issue and I don't need to specify the "canonical" meaning of ...