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pro vyhledávání: '"Subramaniam, Chaitanya Leena"'
Autor:
Subramaniam, Chaitanya Leena
The first part of this dissertation defines "dependently typed algebraic theories", which are a strict subclass of the generalised algebraic theories (GATs) of Cartmell. We characterise dependently typed algebraic theories as finitary monads on certa
Externí odkaz:
http://arxiv.org/abs/2110.02804
We present a variant of the small object argument, inspired by Kelly, better suited to construct unique factorisation systems. Our main result is to compare it to the plus-construction involved in sheafification. We apply this to construct localizati
Externí odkaz:
http://arxiv.org/abs/2004.00731
For $\Lambda$ the category of free opetopic algebras, we construct a model structure \emph{\`a la Cisinski} on the category of presheaves over $\Lambda$, and show that is is equivalent to opetopic complete Segal spaces. This generalizes the results o
Externí odkaz:
http://arxiv.org/abs/2001.07924
We define a family of structures called "opetopic algebras", which are algebraic structures with an underlying opetopic set. Examples of such are categories, planar operads, and Loday's combinads over planar trees. Opetopic algebras can be defined in
Externí odkaz:
http://arxiv.org/abs/1911.00907
For $\Lambda$ the category of free opetopic algebras, we construct a model structure \emph{\`a la Cisinski} on the category of presheaves over $\Lambda$, and show that is is equivalent to opetopic complete Segal spaces. This generalizes the results o
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::62543ee7658524cbf832d9e177dd2fb8
http://arxiv.org/abs/2001.07924
http://arxiv.org/abs/2001.07924