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Homological Transfer between Additive Categories and Higher Differential Additive Categories

Acta Mathematica Sinica, English Series, 2023
Let \(\mathcal C\) be an additive category and \(n\geq 2\) be an integer. The higher differential additive category consists of objects \(X\) in \(\mathcal C\) equipped with an endomorphism \(\varepsilon_X\) satisfying \(\varepsilon_X^n=0.\) Let \(R\) be a finite-dimensional basic algebra over an algebraically closed field, mod\(\,R\) the category of ...
Tang, Xi, Huang, Zhao Yong
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Higher type categories

Mathematical Logic Quarterly, 1993
AbstractHigher types can readily be added to set theory, Bernays‐Morse set theory being an example. A type for each ordinal is added in [2]. Adding higher types to set theory provides a neat solution to the problem of how to handle higher type categories. We give the basic definitions, and prove cocompleteness of some higher type categories. MSC: 14A15.
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Towards Higher Categories

2010
Lectures on -Categories and Cohomology.- A Survey of (#x221E , 1)-Categories.- Internal Categorical Structures in Homotopical Algebra.- A 2-Categories Companion.- Notes on 1- and 2-Gerbes.- An Australian Conspectus of Higher Categories.
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