5 citations · 14 across the 13 of their papers we have counts for
13 papers
Some functorial factorizations for Quillen functors
Hugo Bacard
We prove that any right Quillen functor between arbitrary model categories admits non trivial functorial factorizations that are similar to those of a model structure. We also prov…
Quillen-Segal algebras and Stable homotopy theory
Hugo Bacard
Let be a monoidal model category that is also combinatorial and left proper. If is a monad, operad, properad, or a PROP; following Segal's ideas we deve…
Displacements
Hugo V. Bacard
Given a functor and an object , we define a \emph{displacement} of along a morphism , as a map $e \rightarrow \na…
Symmetries
Hugo V. Bacard
Classical mathematics are founded within set theory, but sets don't have \emph{symmetries}. We conjecture that if we allow sets with symmetries, then many problems such as \emph{Mi…
Understanding higher structures through Quillen-Segal objects
Hugo V. Bacard
If is a model category and is a functor, we defined a Quillen-Segal -object as a weak equivalence $\ma…
Quillen-Segal objects and structures: an overview
Hugo V. Bacard
Let be a combinatorial and left proper model category, possibly with a monoidal structure. If is either a monad on or an operad enriched o…
Model structure on co-Segal commutative dg-algebras in characteristic p>0
Hugo V. Bacard
We study weak commutative algebras in a symmetric monoidal model category . We provide a model structure on these algebras for any symmetric monoidal model category th…
Pursuing Lax Diagrams and Enrichment
Hugo V. Bacard
This paper is part of a project that aims to give a homotopy cousin of Kelly's treatment of enriched category theory. After introducing unital co-Segal M-categories, we establish t…
Toward a strictification theorem for co-Segal categories
Hugo V. Bacard
We show that for a monoidal model category $\M=(\ul{M}, \otimes, I)$, certain co-Segal $\M$-categories are equivalent to strict ones.
A calculus on lax functors
Hugo V. Bacard
We verify that Kelly's constructions of the internal Hom for enriched categories extends naturally to lax functors taking their values in a symmetric monoidal category. Our motivat…
Colax Reedy diagrams
Hugo V. Bacard
We use a theory of colax Reedy diagrams to show that the category of Segal M-precategories with fixed set of objects has a model structure for a symmetric monoidal model category M…
Lax Diagrams and Enrichment
Hugo V. Bacard
We introduce a new type of weakly enriched categories over a given symmetric monoidal model category M; these are called Co-Segal categories. Their definition derives from the phil…
Segal Enriched Categories I
Hugo V. Bacard
We develop a theory of enriched categories over a (higher) category M equipped with a class W of morphisms called homotopy equivalences. We call them Segal M_W -categories. Our mot…