Results 1 to 10 of about 834,273 (109)
The category of opetopes and the category of opetopic sets [PDF]
arXiv, 2003 We give an explicit construction of the category Opetope of opetopes. We prove that the category of opetopic sets is equivalent to the category of presheaves over Opetope.
Cheng, Eugenia
arxiv +3 more sources
Weak omega-categories from intensional type theory [PDF]
Logical Methods in Computer Science, 2010 We show that for any type in Martin-L\"of Intensional Type Theory, the terms of that type and its higher identity types form a weak omega-category in the sense of Leinster.
Peter LeFanu Lumsdaine
doaj +1 more source
Acta Crystallographica Section A: Foundations and Advances, 2021 An invitation to applied category theory seven sketches. p d f an invitation to applied category theory seven. sevensketchesinpositionality. an invitation to applied category theory seven sketches. an invitation to applied category theory seven sketches.
B. Stöger
semanticscholar +1 more source
Semantics of Higher-Order Recursion Schemes [PDF]
Logical Methods in Computer Science, 2011 Higher-order recursion schemes are recursive equations defining new operations from given ones called "terminals". Every such recursion scheme is proved to have a least interpreted semantics in every Scott's model of \lambda-calculus in which the ...
Jiri Adamek, Stefan Milius, Jiri Velebil
doaj +1 more source
Formalizing category theory in Agda
Certified Programs and Proofs, 2021 The generality and pervasiveness of category theory in modern mathematics makes it a frequent and useful target of formalization. It is however quite challenging to formalize, for a variety of reasons. Agda currently (i.e.
Jason Z. S. Hu, J. Carette
semanticscholar +1 more source
Unifying Cubical Models of Univalent Type Theory [PDF]
, 2020 We present a new constructive model of univalent type theory based on cubical sets. Unlike prior work on cubical models, ours depends neither on diagonal cofibrations nor connections.
, Cavallo, Evan, Swan, Andrew W
core +1 more source
The fusion algebra of bimodule categories [PDF]
, 2007 We establish an algebra-isomorphism between the complexified Grothendieck ring F of certain bimodule categories over a modular tensor category and the endomorphism algebra of appropriate morphism spaces of those bimodule categories.
A. Joyal +30 more
core +1 more source
Parametrized higher category theory [PDF]
Algebraic & Geometric Topology, 2018 We develop foundations for the category theory of $\infty$-categories parametrized by a base $\infty$-category. Our main contribution is a theory of indexed homotopy limits and colimits, which specializes to a theory of $G$-colimits for $G$ a finite ...
J. Shah
semanticscholar +1 more source
Pseudo-dualizing complexes and pseudo-derived categories
, 2020 The definition of a pseudo-dualizing complex is obtained from that of a dualizing complex by dropping the injective dimension condition, while retaining the finite generatedness and homothety isomorphism conditions.
Positselski, Leonid
core +1 more source
Morita classes of algebras in modular tensor categories [PDF]
, 2008 We consider algebras in a modular tensor category C. If the trace pairing of an algebra A in C is non-degenerate we associate to A a commutative algebra Z(A), called the full centre, in a doubled version of the category C.
Anderson +34 more
core +2 more sources