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14 votes
1 answer
510 views

What are internal complete atomic boolean algebras, intuitively?

The category of complete atomic boolean algebras $\mathbf{CABA}$ is equivalent to $\mathbf{Set}^{\mathrm{op}}$ via $$\mathbf{Set}^{\mathrm{op}} \to \mathbf{CABA}, ~ X \mapsto (P(X),\bigcup,\bigcap).$$ ...
Martin Brandenburg's user avatar
9 votes
0 answers
539 views

The Curry Howard Isomorphism and models for an intuitionistic modal logic and its bimodal translation

My question regards the Curry Howard Isomorphism and how it constrains models in the case of a particular logic. Consider quantified Lax Logic $QLL$. https://pdfs.semanticscholar.org/468e/...
user65526's user avatar
  • 639
3 votes
2 answers
643 views

Further relation between monads and theories

This question want to be a follow up of the following question. In that thread I was interested in understanding relation between various presentation of algebraic theories. In particular in Eduardo ...
Giorgio Mossa's user avatar
1 vote
0 answers
139 views

Monads for proof relevance in type theory

I am just getting started with homotopy type theory. After watching an introductory lecture, I was attracted to the concept of proof relevance. In my understanding, the core idea here is to elevate ...
Ben Sprott's user avatar
  • 1,313
0 votes
0 answers
110 views

Expressing a model transformation by using monads in the simply-typed lambda calculus

In https://link.springer.com/content/pdf/10.1007/s10670-019-00128-z.pdf , page 16, the following clause is given for a modal operator $\langle R_k \rangle$ (see definition 4.2 for the definition of a ...
user65526's user avatar
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