[HTML][HTML] A synthetic approach to Markov kernels, conditional independence and theorems on sufficient statistics
T Fritz - Advances in Mathematics, 2020 - Elsevier
We develop Markov categories as a framework for synthetic probability and statistics,
following work of Golubtsov as well as Cho and Jacobs. This means that we treat the …
following work of Golubtsov as well as Cho and Jacobs. This means that we treat the …
[图书][B] An invitation to applied category theory: seven sketches in compositionality
Category theory is unmatched in its ability to organize and layer abstractions and to find
commonalities between structures of all sorts. No longer the exclusive preserve of pure …
commonalities between structures of all sorts. No longer the exclusive preserve of pure …
Polynomial functors and polynomial monads
We study polynomial functors over locally cartesian closed categories. After setting up the
basic theory, we show how polynomial functors assemble into a double category, in fact a …
basic theory, we show how polynomial functors assemble into a double category, in fact a …
Seven sketches in compositionality: An invitation to applied category theory
This book is an invitation to discover advanced topics in category theory through concrete,
real-world examples. It aims to give a tour: a gentle, quick introduction to guide later …
real-world examples. It aims to give a tour: a gentle, quick introduction to guide later …
Linear dependent type theory for quantum programming languages
Modern quantum programming languages integrate quantum resources and classical
control. They must, on the one hand, be linearly typed to reflect the no-cloning property of …
control. They must, on the one hand, be linearly typed to reflect the no-cloning property of …
Connections on non-abelian gerbes and their holonomy
U Schreiber, K Waldorf - arXiv preprint arXiv:0808.1923, 2008 - arxiv.org
We introduce an axiomatic framework for the parallel transport of connections on gerbes. It
incorporates parallel transport along curves and along surfaces, and is formulated in terms …
incorporates parallel transport along curves and along surfaces, and is formulated in terms …
A unified framework for generalized multicategories
GSH Cruttwell, MA Shulman - arXiv preprint arXiv:0907.2460, 2009 - arxiv.org
Notions of generalized multicategory have been defined in numerous contexts throughout
the literature, and include such diverse examples as symmetric multicategories, globular …
the literature, and include such diverse examples as symmetric multicategories, globular …
Structured cospans
JC Baez, K Courser - arXiv preprint arXiv:1911.04630, 2019 - arxiv.org
One goal of applied category theory is to better understand networks appearing throughout
science and engineering. Here we introduce" structured cospans" as a way to study …
science and engineering. Here we introduce" structured cospans" as a way to study …
Monoidal grothendieck construction
J Moeller, C Vasilakopoulou - arXiv preprint arXiv:1809.00727, 2018 - arxiv.org
We lift the standard equivalence between fibrations and indexed categories to an
equivalence between monoidal fibrations and monoidal indexed categories, namely weak …
equivalence between monoidal fibrations and monoidal indexed categories, namely weak …
Constructing symmetric monoidal bicategories
MA Shulman - arXiv preprint arXiv:1004.0993, 2010 - arxiv.org
We present a method of constructing symmetric monoidal bicategories from symmetric
monoidal double categories that satisfy a lifting condition. Such symmetric monoidal double …
monoidal double categories that satisfy a lifting condition. Such symmetric monoidal double …