category theory in nLab
Category theory is a toolset for describing the general abstract structures in mathematics. Paradigm. As opposed to set theory, category theory focuses not on ...
A category is a combinatorial model for a directed space – a “directed homotopy 1-type” in some sense. It has “points”, called objects, and also ...
category theory and foundations in nLab
One way to think of category theory is as a framework in which the idea is formalized that every kind of equality is really secretly a choice of ...
The nLab - the (n-)category as a "grand narrative" in mathematics ...
A category is simply a collection of objects and morphisms. In some categories, morphisms represent functions, but in others, they do not.
formal category theory in nLab
Formal category theory may be thought of as applying the philosophy of category theory to category theory itself. Typically, this takes the form ...
The nLab espouses the "n-point of view" (a deliberate pun on Wikipedia's "neutral point of view") that type theory, homotopy theory, category theory, and higher ...
higher category theory in nLab
Higher category theory studies the generalization of ∞-groupoids – and hence, via the homotopy hypothesis, of topological spaces – to that of ...
Is nLab a good source? : r/math - Reddit
nLab presents category theory (and mathematics as a whole) from a very narrow and non-mainstream point of view. I don't think most most working ...
Do Wikipedia, nLab and several books give a wrong definition of ...
Similar formulations are in A First Course in Category Theory by Ana Agore (p. ... 110, “for any other cone”) and nLab (“every other cone”). The ...
relation between type theory and category theory in nLab
We discuss here formalizations and proofs of the relation/equivalence between various flavors of type theories and the corresponding flavors of categories.
category theory in nLab - Unicist News
category theory in nLab ... The unicist theory applied to the evolution of “things” is homologous with the category theory in mathematics. https ...
The nLab espouses the "n-point of view" (a deliberate pun on Wikipedia's "neutral point of view") that type theory, homotopy theory, category theory, and higher ...
Can everything in category theory be restated in a sufficiently ...
Thus a category can be interpreted as an "abstract data structure" and functors between categories are just ordinary (type theoretic) functions ...
Being Tentative on nLab | The n-Category Café
There is also another model structure ((oo,1)-categorial structure) on topological spaces called the Strom-structure. In this structure the weak ...
What non-categorical applications are there of homotopical algebra?
... categories (all that nLab stuff). Here is the sort of ... Is a background in Category Theory enough for starting a PhD in Category Theory?
nLab Category Theory in Context
The text provides tools for understanding and attacking difficult problems in algebra, number theory, algebraic geometry, and algebraic topology.
Just a cautionary note - category theory has seemingly been at ...
In ten words or less: Sets are just 0-categories [7][8]. With more words: Set theory is just 0-category theory. This is obvious today, but two decades ago, ...
I'm truly a fan of the nLab, and I used it a great deal when I was learning some Category Theory. I think it's a great resource and, importantly ...
NLab Memes for〔∞,1〕- categories - Facebook
NLab Memes for〔∞,1〕- categories. 2091 likes · 2 talking about this ... Theory Conference, which was held online this week: https://www.youtube. com ...
From the nLab to the HoTT Book - Sandiego
that category theory and higher category theory provide a point of view on ... Raymond. Page 26. The nLab. Homotopy type theory. The HoTT Book. Conclusions.
Category theory
Category theory is a general theory of mathematical structures and their relations. It was introduced by Samuel Eilenberg and Saunders Mac Lane in the middle of the 20th century in their foundational work on algebraic topology.
Theory of categories
In ontology, the theory of categories concerns itself with the categories of being: the highest genera or kinds of entities. To investigate the categories of being, or simply categories, is to determine the most fundamental and the broadest classes of entities.
Higher category theory
In mathematics, higher category theory is the part of category theory at a higher order, which means that some equalities are replaced by explicit arrows in order to be able to explicitly study the structure behind those equalities.
Category
In mathematics, a category is a collection of "objects" that are linked by "arrows". A category has two basic properties: the ability to compose the arrows associatively and the existence of an identity arrow for each object.
nLab
The nLab is a wiki for research-level notes, expositions and collaborative work, including original research, in mathematics, physics, and philosophy, with a focus on methods from type theory, category theory, and homotopy theory.
Product category
In the mathematical field of category theory, the product of two categories C and D, denoted C × D and called a product category, is an extension of the concept of the Cartesian product of two sets.