categorical semantics of dependent type theory in nLab

Dependent types (in dependent type theory) have categorical semantics given by morphisms which are the bundles whose fibers are the families indexed by the ...

categorical semantics in nLab

Conversely, starting with a given theory of logic or a given type theory, we say that it has a categorical semantics if there is a category such ...

categorical semantics of dependent type theory - nForum

Created categorical model of dependent types, describing the various different ways to strictify category theory to match type theory and their ...

dependent type theory in nLab

1. Idea ... Dependent type theory is the flavor of type theory that admits dependent types. ... is interpreted as a morphism E → X E \to X , hence ...

dependent type in nLab

In type theory, a dependent type or type in context is a family or bundle of types which vary over the elements (terms) of some other type.

What are the motivations for different variants of categorical models ...

I am new to the categorical semantics for dependent type theories, so it is surprising for me to see nLab introduces so many variants of ...

semantics in nLab

Semantics is the interpretation of the syntax of a theory in a model. See a separate page for semantics of a programming language.

Martin-Löf dependent type theory in nLab

Per Martin-Löf's dependent type theory, also known as intuitionistic type theory (Martin-Löf 75), or constructive type theory is a specific form ...

relation between type theory and category theory in nLab

By a syntax-semantics duality one may view type theory as a formal syntactic language or calculus for category theory, and conversely one may ...

Can everything in category theory be restated in a sufficiently ...

As the final issue, the categorical semantics of dependent type theories is complicated (because dependent type theories are complicated). Very ...

The role of category theory in coq proofs - Reddit

... categorical semantics of dependent type theory. https://ncatlab.org/nlab/show/categorical+semantics+of+dependent+type+theory. Upvote 3

Stable homotopy type theory? - hopf algebras - MathOverflow

You may find interesting attempts to form a linear dependent type theory/dependent homotopy type theory, discussed here: ncatlab.org/nlab/show/ ...

type theory in nLab

Explicitly, type theory is a formal language, essentially a set of rules for rewriting certain strings of symbols, that describes the ...

Categorical Semantics of Dependent Type Theory - Daniel Mroz

There is a syntax/semantics duality between type theory and category theory. We can think of type theories as being a formal syntactic system ...

Type theory - Wikipedia

"Theory of types" redirects here. For an architectural term, see Form (architecture) § Theories. In mathematics and theoretical computer science, a type theory ...

Paranatural Category Theory - arXiv

nLab authors. 2023a. categorical semantics of dependent type theory. https://ncatlab.org/nlab/show/categorical+semantics+ · of+dependent+type+ ...

Dependently typed algebraic theories - Wiki - Evan Patterson

Categorical semantics · Overview of dependent types (dependent sums, dependent products, etc) · Shows that categories with attributes are equivalent to categories ...

Stack Semantics | The n-Category Café - Welcome

The ASL is mostly populated with material set theorists and classical logicians, but this year they had a special session on Categorical Logic, ...

How do we construct the Gödel's sentence in Martin-Löf type theory?

In Martin-Löf dependent type theory (MLTT), under the proposition-as-types correspondence, we sometimes say that a proposition A is true if ...

dependent sum type in nLab

In the categorical semantics of dependent type theory in fibration categories, the dependent sum corresponds to internal coproducts over an ...